Single Best Answer MCQs for Sub-Topics of Topic 7: Mensuration

Question 1. Which branch of mathematics deals with the measurement of length, area, and volume of geometric figures?

(A) Algebra

(B) Calculus

(C) Geometry

(D) Mensuration

Question 2. Mensuration is primarily concerned with measuring which properties of shapes?

(A) Only angles

(B) Only shapes and positions

(C) Length, area, and volume

(D) Only symmetry

Question 3. The total length of the boundary of a closed plane figure is called its:

(A) Area

(B) Volume

(C) Perimeter

(D) Circumference

Question 4. The amount of surface enclosed by a closed plane figure is called its:

(A) Perimeter

(B) Area

(C) Volume

(D) Length

Question 5. Which of the following is a standard unit for measuring perimeter?

(A) square metres ($\text{m}^2$)

(B) cubic centimetres ($\text{cm}^3$)

(C) kilometres ($\text{km}$)

(D) square feet ($\text{ft}^2$)

Question 6. Which of the following is a standard unit for measuring area?

(A) metres ($\text{m}$)

(B) cubic metres ($\text{m}^3$)

(C) square centimetres ($\text{cm}^2$)

(D) centimetres ($\text{cm}$)

Question 7. If the perimeter of a square is $20\ \text{cm}$, what is the length of one side?

(A) $4\ \text{cm}$

(B) $5\ \text{cm}$

(C) $10\ \text{cm}$

(D) $2\ \text{cm}$

Question 8. A rectangular field has a length of $15\ \text{m}$ and a width of $10\ \text{m}$. What is its perimeter?

(A) $25\ \text{m}$

(B) $50\ \text{m}$

(C) $150\ \text{m}$

(D) $100\ \text{m}$

Question 9. If the area of a square is $36\ \text{cm}^2$, what is the length of one side?

(A) $4\ \text{cm}$

(B) $6\ \text{cm}$

(C) $9\ \text{cm}$

(D) $12\ \text{cm}$

Question 10. A rectangular room is $8\ \text{m}$ long and $6\ \text{m}$ wide. What is its area?

(A) $14\ \text{m}^2$

(B) $28\ \text{m}^2$

(C) $48\ \text{m}^2$

(D) $24\ \text{m}^2$

Question 11. Converting $5\ \text{metres}$ to centimetres gives:

(A) $0.05\ \text{cm}$

(B) $50\ \text{cm}$

(C) $500\ \text{cm}$

(D) $5000\ \text{cm}$

Question 12. Converting $2\ \text{square metres}$ to square centimetres gives:

(A) $200\ \text{cm}^2$

(B) $2000\ \text{cm}^2$

(C) $20000\ \text{cm}^2$

(D) $200000\ \text{cm}^2$

Question 13. Which unit is generally used to measure the area of a large agricultural field in India?

(A) square centimetres ($\text{cm}^2$)

(B) square metres ($\text{m}^2$)

(C) hectares ($\text{ha}$)

(D) square millimetres ($\text{mm}^2$)

Question 14. One hectare is equal to:

(A) $100\ \text{m}^2$

(B) $1000\ \text{m}^2$

(C) $10000\ \text{m}^2$

(D) $100000\ \text{m}^2$

Question 15. If a shape has a perimeter, it must be a:

(A) Open figure

(B) Closed figure

(C) Solid figure

(D) Straight line

Question 16. If a shape has an area, it must be a:

(A) Three-dimensional figure

(B) One-dimensional figure

(C) Two-dimensional figure

(D) Point

Question 17. The perimeter of a circle is called its:

(A) Area

(B) Diameter

(C) Radius

(D) Circumference

Question 18. Which of the following units is NOT a unit of length (and thus not suitable for perimeter)?

(A) Metre

(B) Kilometre

(C) Acre

(D) Centimetre

Question 19. Which of the following units is NOT a unit of area?

(A) Square metre

(B) Hectare

(C) Litre

(D) Acre

Question 20. Mensuration helps us calculate the space occupied by 3D objects, which is known as:

(A) Area

(B) Perimeter

(C) Surface Area

(D) Volume

Question 1. A triangle has side lengths $a$, $b$, and $c$. What is its perimeter?

(A) $a \times b \times c$

(B) $a + b + c$

(C) $\frac{1}{2} \times \text{base} \times \text{height}$

(D) $\sqrt{s(s-a)(s-b)(s-c)}$

Question 2. A rectangular garden is $25\ \text{m}$ long and $18\ \text{m}$ wide. A fence is to be built around it. What length of fencing is required?

(A) $43\ \text{m}$

(B) $86\ \text{m}$

(C) $450\ \text{m}$

(D) $172\ \text{m}$

Question 3. The side length of a square park is $60\ \text{m}$. What is the perimeter of the park?

(A) $120\ \text{m}$

(B) $240\ \text{m}$

(C) $3600\ \text{m}$

(D) $30\ \text{m}$

Question 4. The adjacent sides of a parallelogram are $12\ \text{cm}$ and $9\ \text{cm}$. What is the perimeter of the parallelogram?

(A) $21\ \text{cm}$

(B) $42\ \text{cm}$

(C) $108\ \text{cm}$

(D) $54\ \text{cm}$

Question 5. A regular pentagon has a side length of $7\ \text{cm}$. What is its perimeter?

(A) $35\ \text{cm}$

(B) $28\ \text{cm}$

(C) $42\ \text{cm}$

(D) $49\ \text{cm}$

Question 6. The perimeter of a rectangle is $60\ \text{cm}$. If the length is $20\ \text{cm}$, what is the width?

(A) $10\ \text{cm}$

(B) $15\ \text{cm}$

(C) $20\ \text{cm}$

(D) $40\ \text{cm}$

Question 7. The perimeter of a square is $100\ \text{m}$. What is the length of its side?

(A) $20\ \text{m}$

(B) $25\ \text{m}$

(C) $50\ \text{m}$

(D) $10\ \text{m}$

Question 8. A triangular field has sides measuring $8\ \text{m}$, $15\ \text{m}$, and $17\ \text{m}$. What is the perimeter of the field?

(A) $30\ \text{m}$

(B) $40\ \text{m}$

(C) $34\ \text{m}$

(D) $60\ \text{m}$

Question 9. A wire is bent into the shape of a square of side $10\ \text{cm}$. If the same wire is bent into a rectangle of length $12\ \text{cm}$, what is the width of the rectangle?

(A) $8\ \text{cm}$

(B) $10\ \text{cm}$

(C) $16\ \text{cm}$

(D) $14\ \text{cm}$

Question 10. The perimeter of a rhombus is $52\ \text{cm}$. What is the length of each side?

(A) $13\ \text{cm}$

(B) $26\ \text{cm}$

(C) $10.4\ \text{cm}$

(D) $4\ \text{cm}$

Question 11. An isosceles triangle has a perimeter of $30\ \text{cm}$. If the unequal side is $10\ \text{cm}$, what is the length of each of the equal sides?

(A) $10\ \text{cm}$

(B) $15\ \text{cm}$

(C) $20\ \text{cm}$

(D) $5\ \text{cm}$

Question 12. The ratio of the sides of a rectangle is $5:3$. If its perimeter is $64\ \text{cm}$, what is the length of the longer side?

(A) $12\ \text{cm}$

(B) $16\ \text{cm}$

(C) $20\ \text{cm}$

(D) $40\ \text{cm}$

Question 13. A perimeter is a measure of:

(A) One-dimensional extent

(B) Two-dimensional extent

(C) Three-dimensional extent

(D) Surface area

Question 14. How many times must a person walk around a square field of side $50\ \text{m}$ to cover a distance of $2\ \text{km}$?

(A) 5 times

(B) 10 times

(C) 20 times

(D) 4 times

Question 15. The perimeter of a parallelogram with sides $a$ and $b$ is:

(A) $a+b$

(B) $a \times b$

(C) $2(a+b)$

(D) $a^2 + b^2$

Question 16. A polygon has $n$ sides, each of length $s$. If it is a regular polygon, what is its perimeter?

(A) $s+n$

(B) $s/n$

(C) $n/s$

(D) $n \times s$

Question 17. The perimeter of a rectangle is $P$ and its length is $l$. What is its width $w$?

(A) $w = P - 2l$

(B) $w = P/2 - l$

(C) $w = (P-l)/2$

(D) $w = P/2 + l$

Question 18. If the perimeter of an equilateral triangle is $45\ \text{cm}$, what is the length of each side?

(A) $9\ \text{cm}$

(B) $15\ \text{cm}$

(C) $22.5\ \text{cm}$

(D) $45\ \text{cm}$

Question 19. The perimeter of a plot of land is $300\ \text{m}$. If the plot is square-shaped, what is the length of its side?

(A) $75\ \text{m}$

(B) $150\ \text{m}$

(C) $100\ \text{m}$

(D) $50\ \text{m}$

Question 20. A path runs along the boundary of a rectangular park. If the park is $50\ \text{m}$ long and $30\ \text{m}$ wide, what is the total length of the path?

(A) $80\ \text{m}$

(B) $160\ \text{m}$

(C) $1500\ \text{m}$

(D) $100\ \text{m}$

Question 1. What is the area of a square with side length $15\ \text{cm}$?

(A) $30\ \text{cm}^2$

(B) $60\ \text{cm}^2$

(C) $150\ \text{cm}^2$

(D) $225\ \text{cm}^2$

Question 2. A rectangular piece of land is $40\ \text{m}$ long and $25\ \text{m}$ wide. What is its area?

(A) $65\ \text{m}^2$

(B) $130\ \text{m}^2$

(C) $1000\ \text{m}^2$

(D) $800\ \text{m}^2$

Question 3. The base of a parallelogram is $10\ \text{cm}$ and its corresponding height is $6\ \text{cm}$. What is its area?

(A) $16\ \text{cm}^2$

(B) $32\ \text{cm}^2$

(C) $60\ \text{cm}^2$

(D) $120\ \text{cm}^2$

Question 4. What is the area of a triangle with base $8\ \text{cm}$ and height $5\ \text{cm}$?

(A) $13\ \text{cm}^2$

(B) $40\ \text{cm}^2$

(C) $20\ \text{cm}^2$

(D) $26\ \text{cm}^2$

Question 5. If the area of a rectangle is $120\ \text{cm}^2$ and its length is $15\ \text{cm}$, what is its width?

(A) $8\ \text{cm}$

(B) $10\ \text{cm}$

(C) $12\ \text{cm}$

(D) $16\ \text{cm}$

Question 6. The area of a square field is $2500\ \text{m}^2$. What is the length of its side?

(A) $25\ \text{m}$

(B) $50\ \text{m}$

(C) $100\ \text{m}$

(D) $625\ \text{m}$

Question 7. A triangle and a parallelogram have the same base and the same area. If the height of the triangle is $10\ \text{cm}$, what is the height of the parallelogram?

(A) $5\ \text{cm}$

(B) $10\ \text{cm}$

(C) $20\ \text{cm}$

(D) $15\ \text{cm}$

Question 8. A field is in the shape of a trapezium. Its parallel sides are $10\ \text{m}$ and $16\ \text{m}$, and the perpendicular distance between them is $8\ \text{m}$. What is the area of the trapezium?

(A) $104\ \text{m}^2$

(B) $64\ \text{m}^2$

(C) $208\ \text{m}^2$

(D) $128\ \text{m}^2$

Question 9. If the base of a triangle is doubled and its height is halved, how does its area change?

(A) Area is doubled

(B) Area is halved

(C) Area remains the same

(D) Area becomes four times

Question 10. The diagonal of a square is $10\ \text{cm}$. What is its area?

(A) $100\ \text{cm}^2$

(B) $50\ \text{cm}^2$

(C) $25\ \text{cm}^2$

(D) $200\ \text{cm}^2$

Question 11. A parallelogram has an area of $150\ \text{cm}^2$ and its base is $15\ \text{cm}$. What is its corresponding height?

(A) $10\ \text{cm}$

(B) $15\ \text{cm}$

(C) $20\ \text{cm}$

(D) $30\ \text{cm}$

Question 12. The cost of levelling a rectangular plot is $\textsf{₹}\, 5000$ at the rate of $\textsf{₹}\, 5$ per square metre. If the length of the plot is $50\ \text{m}$, what is its width?

(A) $10\ \text{m}$

(B) $20\ \text{m}$

(C) $25\ \text{m}$

(D) $50\ \text{m}$

Question 13. Two rectangles have the same area. The first rectangle has length $16\ \text{cm}$ and width $10\ \text{cm}$. The second rectangle has length $20\ \text{cm}$. What is the width of the second rectangle?

(A) $8\ \text{cm}$

(B) $12\ \text{cm}$

(C) $15\ \text{cm}$

(D) $18\ \text{cm}$

Question 14. The area of a right-angled triangle is $60\ \text{cm}^2$. If its base is $15\ \text{cm}$, what is its height?

(A) $4\ \text{cm}$

(B) $8\ \text{cm}$

(C) $12\ \text{cm}$

(D) $10\ \text{cm}$

Question 15. A square and a rectangle have the same perimeter. The side of the square is $10\ \text{cm}$. The length of the rectangle is $12\ \text{cm}$. Which figure has a larger area?

(A) Square

(B) Rectangle

(C) Both have the same area

(D) Cannot be determined

Question 16. A parallelogram has a base of $x\ \text{units}$ and a corresponding height of $y\ \text{units}$. Its area is:

(A) $x+y$ square units

(B) $x \times y$ square units

(C) $\frac{1}{2} x y$ square units

(D) $2(x+y)$ square units

Question 17. If the base of a triangle is $b$ and its area is $A$, what is its height $h$?

(A) $h = 2A/b$

(B) $h = A/b$

(C) $h = 2Ab$

(D) $h = b/(2A)$

Question 18. The area of a parallelogram with adjacent sides $a$ and $b$ can be calculated as $a \times h$, where $h$ is the height corresponding to side $a$. What about the other adjacent side $b$?

(A) The height corresponding to side $b$ is also $h$.

(B) The height corresponding to side $b$ is $a \times h / b$.

(C) The area is also $b \times h$.

(D) The area is $\frac{1}{2} b \times h$.

Question 19. A rectangular lawn is $30\ \text{m}$ by $20\ \text{m}$. It is to be paved with tiles of size $60\ \text{cm}$ by $50\ \text{cm}$. How many tiles are needed?

(A) 2000 tiles

(B) 1000 tiles

(C) 500 tiles

(D) 200 tiles

Question 20. The area of a triangle is $48\ \text{cm}^2$. If the base is $12\ \text{cm}$, the height is:

(A) $4\ \text{cm}$

(B) $6\ \text{cm}$

(C) $8\ \text{cm}$

(D) $10\ \text{cm}$

Question 1. Heron's formula is used to calculate the area of a triangle when:

(A) Only the base and height are known

(B) It is a right-angled triangle

(C) The lengths of all three sides are known

(D) It is an equilateral triangle

Question 2. For a triangle with sides $a, b, c$, the semi-perimeter $s$ is given by:

(A) $s = a+b+c$

(B) $s = \frac{a+b+c}{2}$

(C) $s = \sqrt{a+b+c}$

(D) $s = 2(a+b+c)$

Question 3. Heron's formula for the area of a triangle with sides $a, b, c$ and semi-perimeter $s$ is:

(A) Area $= s(s-a)(s-b)(s-c)$

(B) Area $= \sqrt{s(s-a)(s-b)(s-c)}$

(C) Area $= (s-a)(s-b)(s-c)$

(D) Area $= s^2(s-a)(s-b)(s-c)$

Question 4. A triangle has sides of length $3\ \text{cm}$, $4\ \text{cm}$, and $5\ \text{cm}$. What is its semi-perimeter?

(A) $6\ \text{cm}$

(B) $12\ \text{cm}$

(C) $7.5\ \text{cm}$

(D) $10\ \text{cm}$

Question 5. What is the area of the triangle with sides $3\ \text{cm}$, $4\ \text{cm}$, and $5\ \text{cm}$ using Heron's formula?

(A) $6\ \text{cm}^2$

(B) $12\ \text{cm}^2$

(C) $7.5\ \text{cm}^2$

(D) $10\ \text{cm}^2$

Question 6. The sides of a triangular field are $50\ \text{m}$, $80\ \text{m}$, and $120\ \text{m}$. Can you find its area using Heron's formula?

(A) Yes, calculate $s = (50+80+120)/2$ and use the formula.

(B) No, because the sum of two sides is not greater than the third side.

(C) Yes, but only if it is a right-angled triangle.

(D) No, Heron's formula is only for equilateral triangles.

Question 7. For an equilateral triangle with side length $a$, what is its semi-perimeter?

(A) $a/2$

(B) $3a$

(C) $3a/2$

(D) $a^2$

Question 8. Using Heron's formula, the area of an equilateral triangle with side $a$ is:

(A) $\frac{\sqrt{3}}{4}a^2$

(B) $\frac{1}{2}a^2$

(C) $a^2$

(D) $\sqrt{3}a^2$

Question 9. An isosceles triangle has equal sides of length $13\ \text{cm}$ and a base of $10\ \text{cm}$. What is its semi-perimeter?

(A) $36\ \text{cm}$

(B) $18\ \text{cm}$

(C) $16\ \text{cm}$

(D) $14\ \text{cm}$

Question 10. What is the area of the isosceles triangle with sides $13\ \text{cm}$, $13\ \text{cm}$, and $10\ \text{cm}$ using Heron's formula?

(A) $30\ \text{cm}^2$

(B) $60\ \text{cm}^2$

(C) $78\ \text{cm}^2$

(D) $156\ \text{cm}^2$

Question 11. The perimeter of a triangle is $42\ \text{cm}$. Two of its sides are $15\ \text{cm}$ and $13\ \text{cm}$. What is the length of the third side?

(A) $14\ \text{cm}$

(B) $10\ \text{cm}$

(C) $12\ \text{cm}$

(D) $16\ \text{cm}$

Question 12. What is the area of the triangle described in Question 11 using Heron's formula?

(A) $84\ \text{cm}^2$

(B) $42\ \text{cm}^2$

(C) $64\ \text{cm}^2$

(D) $72\ \text{cm}^2$

Question 13. The ratio of the sides of a triangle is $3:4:5$. If its perimeter is $36\ \text{cm}$, what is the area of the triangle?

(A) $54\ \text{cm}^2$

(B) $72\ \text{cm}^2$

(C) $108\ \text{cm}^2$

(D) $216\ \text{cm}^2$

Question 14. Heron's formula is derived from:

(A) Pythagorean theorem

(B) Trigonometry formulas (like cosine rule)

(C) Basic area formula ($\frac{1}{2} \times \text{base} \times \text{height}$)

(D) All of the above

Question 15. An equilateral triangle has an area of $16\sqrt{3}\ \text{cm}^2$. What is the length of its side?

(A) $4\ \text{cm}$

(B) $8\ \text{cm}$

(C) $12\ \text{cm}$

(D) $16\ \text{cm}$

Question 16. An isosceles triangle has a perimeter of $40\ \text{cm}$ and its equal sides are $13\ \text{cm}$ each. What is the area of the triangle?

(A) $30\ \text{cm}^2$

(B) $60\ \text{cm}^2$

(C) $90\ \text{cm}^2$

(D) $120\ \text{cm}^2$

Question 17. The sides of a triangle are $11\ \text{cm}$, $60\ \text{cm}$, and $61\ \text{cm}$. What is the area of this triangle?

(A) $180\ \text{cm}^2$

(B) $330\ \text{cm}^2$

(C) $660\ \text{cm}^2$

(D) $900\ \text{cm}^2$

Question 18. A triangular park has sides $120\ \text{m}$, $170\ \text{m}$, and $250\ \text{m}$. What is its semi-perimeter?

(A) $270\ \text{m}$

(B) $540\ \text{m}$

(C) $300\ \text{m}$

(D) $180\ \text{m}$

Question 19. What is the area of the triangular park described in Question 18?

(A) $900\ \text{m}^2$

(B) $1800\ \text{m}^2$

(C) $9000\ \text{m}^2$

(D) $18000\ \text{m}^2$

Question 20. If the sides of a triangle are $a, b, c$, and $s = \frac{a+b+c}{2}$, under what condition is the area $0$ using Heron's formula?

(A) If $a=b=c$

(B) If $a^2+b^2=c^2$

(C) If $a+b \le c$ (or any triangle inequality violated)

(D) The area is never $0$ for a triangle

Question 1. A general quadrilateral has a diagonal of length $d$. Perpendiculars are drawn from the opposite vertices to this diagonal, with lengths $h_1$ and $h_2$. What is the area of the quadrilateral?

(A) $d(h_1+h_2)$

(B) $\frac{1}{2} d(h_1+h_2)$

(C) $d \times h_1 \times h_2$

(D) $\frac{1}{2} d h_1 h_2$

Question 2. The diagonals of a rhombus are $16\ \text{cm}$ and $12\ \text{cm}$. What is the area of the rhombus?

(A) $192\ \text{cm}^2$

(B) $96\ \text{cm}^2$

(C) $48\ \text{cm}^2$

(D) $28\ \text{cm}^2$

Question 3. A kite has diagonals of length $d_1$ and $d_2$. What is its area?

(A) $d_1 d_2$

(B) $2 d_1 d_2$

(C) $\frac{1}{2}(d_1+d_2)$

(D) $\frac{1}{2} d_1 d_2$

Question 4. A quadrilateral ABCD has a diagonal AC of length $20\ \text{cm}$. The perpendiculars from B and D to AC are $8\ \text{cm}$ and $12\ \text{cm}$ respectively. What is the area of the quadrilateral?

(A) $200\ \text{cm}^2$

(B) $400\ \text{cm}^2$

(C) $160\ \text{cm}^2$

(D) $240\ \text{cm}^2$

Question 5. To find the area of a quadrilateral by dividing it into two triangles using a diagonal, which formula(s) can be applied to the triangles?

(A) Only $\frac{1}{2} \times \text{base} \times \text{height}$ if height to the diagonal is known.

(B) Only Heron's formula if all side lengths of the triangles are known.

(C) Either $\frac{1}{2} \times \text{base} \times \text{height}$ or Heron's formula, depending on available information.

(D) Neither, a different method is needed for quadrilaterals.

Question 6. A rhombus has a side length of $10\ \text{cm}$ and one diagonal is $16\ \text{cm}$. What is the length of the other diagonal?

(A) $10\ \text{cm}$

(B) $12\ \text{cm}$

(C) $14\ \text{cm}$

(D) $16\ \text{cm}$

Question 7. What is the area of the rhombus described in Question 6?

(A) $120\ \text{cm}^2$

(B) $96\ \text{cm}^2$

(C) $80\ \text{cm}^2$

(D) $60\ \text{cm}^2$

Question 8. A quadrilateral ABCD has sides AB=9m, BC=12m, CD=5m, DA=8m and diagonal AC=15m. To find its area, you can:

(A) Directly use the formula for a general quadrilateral with one diagonal.

(B) Calculate the area of triangle ABC and triangle ADC using Heron's formula and sum them up.

(C) It is not possible to find the area with this information.

(D) Assume it is a parallelogram and use base $\times$ height.

Question 9. For the quadrilateral in Question 8, find the area of triangle ABC (sides 9, 12, 15).

(A) $54\ \text{m}^2$

(B) $45\ \text{m}^2$

(C) $60\ \text{m}^2$

(D) $72\ \text{m}^2$

Question 10. For the quadrilateral in Question 8, find the area of triangle ADC (sides 15, 5, 8).

(A) $12\ \text{m}^2$

(B) $18\ \text{m}^2$

(C) $20\ \text{m}^2$

(D) This triangle is not possible with these side lengths.

Question 11. What is the total area of the quadrilateral ABCD in Question 8?

(A) $66\ \text{m}^2$

(B) $72\ \text{m}^2$

(C) $74\ \text{m}^2$

(D) $68\ \text{m}^2$

Question 12. To find the area of a general polygon (more than 4 sides), a common method is to:

(A) Use a single formula involving all side lengths.

(B) Divide it into non-overlapping triangles and sum their areas.

(C) Multiply the perimeter by a constant factor.

(D) There is no general method.

Question 13. A field is in the shape of a regular hexagon with side length $10\ \text{m}$. How can you find its area?

(A) Divide it into 6 equilateral triangles and find their sum.

(B) Divide it into a rectangle and two triangles.

(C) Use the formula for the area of a rhombus.

(D) Multiply the perimeter by the side length.

Question 14. What is the area of a regular hexagon with side length $a$?

(A) $\frac{\sqrt{3}}{4}a^2$

(B) $\frac{3\sqrt{3}}{2}a^2$

(C) $6a^2$

(D) $3\sqrt{3}a^2$

Question 15. A parallelogram has diagonals $d_1$ and $d_2$ that intersect at right angles. This parallelogram is a:

(A) Rectangle

(B) Square

(C) Rhombus

(D) Trapezium

Question 16. The area of a rhombus is $216\ \text{cm}^2$. If one diagonal is $18\ \text{cm}$, what is the length of the other diagonal?

(A) $12\ \text{cm}$

(B) $16 \ \text{cm}$

(C) $24\ \text{cm}$

(D) $36\ \text{cm}$

Question 17. A field in the shape of a rhombus has diagonals $14\ \text{m}$ and $20\ \text{m}$. What is the area of the field?

(A) $70\ \text{m}^2$

(B) $140\ \text{m}^2$

(C) $280\ \text{m}^2$

(D) $34\ \text{m}^2$

Question 18. To find the area of a polygon using the triangulation method, you:

(A) Draw a single diagonal and calculate two triangle areas.

(B) Draw diagonals from one vertex to all non-adjacent vertices and sum the areas of the resulting triangles.

(C) Divide the polygon into rectangles and squares only.

(D) Use a specific formula for each type of polygon.

Question 19. A kite has diagonals $d_1$ and $d_2$. If $d_1 = 10\ \text{cm}$ and the area is $60\ \text{cm}^2$, what is the length of the other diagonal $d_2$?

(A) $6\ \text{cm}$

(B) $12\ \text{cm}$

(C) $8\ \text{cm}$

(D) $10\ \text{cm}$

Question 20. The area of a regular octagon with side length $a$ can be calculated by dividing it into triangles. How many identical isosceles triangles meeting at the center can it be divided into?

(A) 6

(B) 8

(C) 10

(D) 12

Question 1. The circumference of a circle is the same as its:

(A) Area

(B) Diameter

(C) Perimeter

(D) Radius

Question 2. The formula for the circumference of a circle with radius $r$ is:

(A) $\pi r^2$

(B) $2\pi r$

(C) $\pi d$

(D) Both (B) and (C) where $d=2r$

Question 3. The formula for the area of a circle with radius $r$ is:

(A) $2\pi r$

(B) $\pi r^2$

(C) $\frac{1}{2} \pi r^2$

(D) $\pi d$

Question 4. The diameter of a wheel is $84\ \text{cm}$. What is its circumference? (Use $\pi = \frac{22}{7}$)

(A) $132\ \text{cm}$

(B) $264\ \text{cm}$

(C) $441\ \text{cm}$

(D) $528\ \text{cm}$

Question 5. What is the area of a circle with radius $7\ \text{cm}$? (Use $\pi = \frac{22}{7}$)

(A) $22\ \text{cm}^2$

(B) $44\ \text{cm}^2$

(C) $154\ \text{cm}^2$

(D) $308\ \text{cm}^2$

Question 6. If the circumference of a circle is $88\ \text{cm}$, what is its radius? (Use $\pi = \frac{22}{7}$)

(A) $7\ \text{cm}$

(B) $14\ \text{cm}$

(C) $21\ \text{cm}$

(D) $28\ \text{cm}$

Question 7. If the area of a circle is $616\ \text{cm}^2$, what is its radius? (Use $\pi = \frac{22}{7}$)

(A) $7\ \text{cm}$

(B) $14\ \text{cm}$

(C) $21\ \text{cm}$

(D) $28\ \text{cm}$

Question 8. The ratio of the circumference to the diameter of a circle is always equal to:

(A) $2$

(B) $\pi$

(C) $\pi/2$

(D) $\pi^2$

Question 9. If the radius of a circle is doubled, how does its area change?

(A) Area is doubled

(B) Area is halved

(C) Area becomes four times

(D) Area remains the same

Question 10. If the diameter of a circle is $14\ \text{cm}$, what is its area? (Use $\pi = \frac{22}{7}$)

(A) $154\ \text{cm}^2$

(B) $44\ \text{cm}^2$

(C) $77\ \text{cm}^2$

(D) $308\ \text{cm}^2$

Question 11. A wire is in the shape of a circle with radius $21\ \text{cm}$. If it is bent into a square, what is the side length of the square? (Use $\pi = \frac{22}{7}$)

(A) $11\ \text{cm}$

(B) $22\ \text{cm}$

(C) $33\ \text{cm}$

(D) $44\ \text{cm}$

Question 12. The area of a circular garden is $3850\ \text{m}^2$. What is its radius? (Use $\pi = \frac{22}{7}$)

(A) $25\ \text{m}$

(B) $30\ \text{m}$

(C) $35\ \text{m}$

(D) $40\ \text{m}$

Question 13. The ratio of the areas of two circles is $4:9$. What is the ratio of their radii?

(A) $2:3$

(B) $4:9$

(C) $16:81$

(D) $3:2$

Question 14. The ratio of the circumferences of two circles is $5:7$. What is the ratio of their areas?

(A) $5:7$

(B) $7:5$

(C) $25:49$

(D) $49:25$

Question 15. How many revolutions will a wheel of diameter $56\ \text{cm}$ make to travel a distance of $176\ \text{m}$? (Use $\pi = \frac{22}{7}$)

(A) 50 revolutions

(B) 100 revolutions

(C) 1000 revolutions

(D) 500 revolutions

Question 16. The radius of a circle is $r$. If its circumference is equal to the perimeter of a square, what is the side length of the square in terms of $r$?

(A) $\pi r$

(B) $\pi r / 2$

(C) $2\pi r$

(D) $\pi r / 4$

Question 17. The area of a circular ring formed by two concentric circles with radii $R$ (outer) and $r$ (inner) is:

(A) $\pi R^2 - \pi r^2$

(B) $\pi (R-r)^2$

(C) $2\pi (R-r)$

(D) $2\pi R - 2\pi r$

Question 18. A path of width $w$ runs around a circular park of radius $r$. What is the area of the path?

(A) $\pi (r+w)^2 - \pi r^2$

(B) $\pi w^2$

(C) $2\pi r w$

(D) $\pi (r+w)^2$

Question 19. If the circumference of a circle is equal to its area, what is the radius of the circle?

(A) 1 unit

(B) 2 units

(C) $\pi$ units

(D) $2\pi$ units

Question 20. The radius of a bicycle wheel is $35\ \text{cm}$. How much distance does it cover in 100 revolutions? (Use $\pi = \frac{22}{7}$)

(A) $220\ \text{m}$

(B) $110\ \text{m}$

(C) $2200\ \text{cm}$

(D) $1100\ \text{cm}$

Question 1. A sector of a circle is the region enclosed by:

(A) An arc and a chord

(B) Two radii and an arc

(C) Two chords and an arc

(D) Two tangents and an arc

Question 2. The length of an arc of a sector with radius $r$ and angle $\theta$ (in degrees) is given by:

(A) $\frac{\theta}{360} \times \pi r^2$

(B) $\frac{\theta}{360} \times 2\pi r$

(C) $\frac{360}{\theta} \times 2\pi r$

(D) $\frac{\theta}{180} \times \pi r$

Question 3. The area of a sector of a circle with radius $r$ and angle $\theta$ (in degrees) is given by:

(A) $\frac{\theta}{360} \times 2\pi r$

(B) $\frac{\theta}{360} \times \pi r^2$

(C) $\frac{\theta}{180} \times \pi r^2$

(D) $\frac{360}{\theta} \times \pi r^2$

Question 4. A circle has a radius of $10\ \text{cm}$. What is the area of a sector with a central angle of $90^\circ$? (Use $\pi = 3.14$)

(A) $31.4\ \text{cm}^2$

(B) $78.5\ \text{cm}^2$

(C) $157\ \text{cm}^2$

(D) $314\ \text{cm}^2$

Question 5. What is the length of the arc of the sector described in Question 4?

(A) $15.7\ \text{cm}$

(B) $31.4\ \text{cm}$

(C) $7.85\ \text{cm}$

(D) $6.28\ \text{cm}$

Question 6. A segment of a circle is the region enclosed by:

(A) Two radii and an arc

(B) A chord and an arc

(C) Two chords and a radius

(D) The diameter and a chord

Question 7. The area of a minor segment of a circle is given by:

(A) Area of the corresponding sector $+$ Area of the corresponding triangle

(B) Area of the corresponding sector $-$ Area of the corresponding triangle

(C) Area of the circle $-$ Area of the minor segment

(D) Area of the major sector $-$ Area of the major triangle

Question 8. A chord of a circle of radius $14\ \text{cm}$ subtends a right angle at the centre. What is the area of the corresponding minor sector? (Use $\pi = \frac{22}{7}$)

(A) $77\ \text{cm}^2$

(B) $154\ \text{cm}^2$

(C) $308\ \text{cm}^2$

(D) $616\ \text{cm}^2$

Question 9. For the scenario in Question 8, what is the area of the triangle formed by the radii and the chord?

(A) $49\ \text{cm}^2$

(B) $98\ \text{cm}^2$

(C) $196\ \text{cm}^2$

(D) $77\ \text{cm}^2$

Question 10. For the scenario in Question 8, what is the area of the corresponding minor segment?

(A) $77\ \text{cm}^2 - 98\ \text{cm}^2$

(B) $154\ \text{cm}^2 - 98\ \text{cm}^2$

(C) $154\ \text{cm}^2 + 98\ \text{cm}^2$

(D) $77\ \text{cm}^2 + 98\ \text{cm}^2$

Question 11. The angle of a sector is $60^\circ$ and the radius is $7\ \text{cm}$. What is the area of the sector? (Use $\pi = \frac{22}{7}$)

(A) $77/3\ \text{cm}^2$

(B) $154/3\ \text{cm}^2$

(C) $77\ \text{cm}^2$

(D) $154\ \text{cm}^2$

Question 12. What is the length of the arc of the sector described in Question 11?

(A) $11\ \text{cm}$

(B) $22/3\ \text{cm}$

(C) $44/3\ \text{cm}$

(D) $22\ \text{cm}$

Question 13. The area of a sector is $\frac{1}{6}$th of the area of the circle. What is the central angle of the sector?

(A) $30^\circ$

(B) $45^\circ$

(C) $60^\circ$

(D) $90^\circ$

Question 14. The perimeter of a sector with radius $r$ and arc length $l$ is:

(A) $r + l$

(B) $2r + l$

(C) $\frac{1}{2} r l$

(D) $\pi r^2 \times \frac{l}{2\pi r}$

Question 15. The area of a sector with radius $r$ and arc length $l$ can also be given by:

(A) $r \times l$

(B) $2r + l$

(C) $\frac{1}{2} r l$

(D) $r^2 l$

Question 16. The area of a major sector is the area of the circle minus the area of the minor sector. True or False?

(A) True

(B) False

(C) Depends on the angle

(D) Only for semicircle

Question 17. The area of a major segment is the area of the circle minus the area of the minor segment. True or False?

(A) True

(B) False

(C) Depends on the chord

(D) Only for diameter

Question 18. The radius of a circular park is $20\ \text{m}$. A sectorial area for children's play is created with a central angle of $108^\circ$. What is the area of this play area? (Use $\pi = 3.14$)

(A) $376.8\ \text{m}^2$

(B) $753.6\ \text{m}^2$

(C) $1130.4\ \text{m}^2$

(D) $1507.2\ \text{m}^2$

Question 19. A minute hand of a clock is $15\ \text{cm}$ long. How far does the tip of the minute hand move in 20 minutes? (Use $\pi = 3.14$)

(A) $15.7\ \text{cm}$

(B) $31.4\ \text{cm}$

(C) $47.1\ \text{cm}$

(D) $62.8\ \text{cm}$

Question 20. A chord of a circle of radius $10\ \text{cm}$ makes a right angle at the centre. The area of the minor segment is (Use $\pi = 3.14$):

(A) $28.5\ \text{cm}^2$

(B) $78.5\ \text{cm}^2$

(C) $50\ \text{cm}^2$

(D) $128.5\ \text{cm}^2$

Question 1. To find the area of a composite figure formed by combining basic shapes, you generally:

(A) Add the areas of the basic shapes if they don't overlap.

(B) Subtract the areas of overlapping regions.

(C) Add or subtract areas as needed, depending on how the shapes are combined.

(D) Find the perimeter and multiply it by a factor.

Question 2. To find the perimeter of a composite figure, you generally:

(A) Add the perimeters of all the basic shapes involved.

(B) Sum the lengths of only the outer boundary of the combined figure.

(C) Subtract the lengths of any internal lines.

(D) Find the area and take its square root.

Question 3. A rectangular garden is $10\ \text{m}$ by $15\ \text{m}$. A path of width $2\ \text{m}$ is built around it. What is the area of the path?

(A) $50\ \text{m}^2$

(B) $100\ \text{m}^2$

(C) $150\ \text{m}^2$

(D) $196\ \text{m}^2$

Question 4. Two squares of side $5\ \text{cm}$ are joined together along one side. What is the perimeter of the resulting figure?

(A) $40\ \text{cm}$

(B) $30\ \text{cm}$

(C) $25\ \text{cm}$

(D) $50\ \text{cm}$

Question 5. What is the area of the composite figure described in Question 4?

(A) $25\ \text{cm}^2$

(B) $50\ \text{cm}^2$

(C) $75\ \text{cm}^2$

(D) $100\ \text{cm}^2$

Question 6. A rectangular park is $20\ \text{m}$ long and $10\ \text{m}$ wide. Two paths, each $1\ \text{m}$ wide, are built parallel to the length and width, intersecting at the centre. What is the area of the paths?

(A) $30\ \text{m}^2$

(B) $29\ \text{m}^2$

(C) $200\ \text{m}^2$

(D) $21\ \text{m}^2$

Question 7. A semicircle is attached to the side of a square of side $7\ \text{cm}$. What is the perimeter of the composite figure? (Use $\pi = \frac{22}{7}$)

(A) $28\ \text{cm}$

(B) $22\ \text{cm}$

(C) $36\ \text{cm}$

(D) $39\ \text{cm}$

Question 8. What is the area of the composite figure described in Question 7?

(A) $49\ \text{cm}^2$

(B) $38.5\ \text{cm}^2$

(C) $87.5\ \text{cm}^2$

(D) $122.5\ \text{cm}^2$

Question 9. A circle is inscribed in a square of side $a$. The area of the region between the square and the circle is:

(A) $a^2 - \pi a^2$

(B) $a^2 - \pi (\frac{a}{2})^2$

(C) $\pi (\frac{a}{2})^2 - a^2$

(D) $a^2 - \pi a$

Question 10. A flower bed is in the shape of a circle of radius $7\ \text{m}$. A path of width $3\ \text{m}$ surrounds it. What is the area of the path? (Use $\pi = \frac{22}{7}$)

(A) $110\ \text{m}^2$

(B) $132\ \text{m}^2$

(C) $188\ \text{m}^2$

(D) $210\ \text{m}^2$

Question 11. A square plot of side $10\ \text{m}$ has a $1\ \text{m}$ wide path running inside along its boundary. What is the area of the path?

(A) $36\ \text{m}^2$

(B) $40\ \text{m}^2$

(C) $100\ \text{m}^2$

(D) $64\ \text{m}^2$

Question 12. Three semicircles are drawn on the sides of a right-angled triangle with sides $6\ \text{cm}$, $8\ \text{cm}$, and $10\ \text{cm}$ as diameters. What is the area of the region enclosed between the largest semicircle and the two smaller semicircles?

(A) Area of the triangle

(B) Sum of the areas of the two smaller semicircles

(C) Area of the largest semicircle

(D) Sum of the areas of the two smaller semicircles minus the area of the triangle

Question 13. Two circles of radius $r$ each are placed such that the centre of each lies on the circumference of the other. What is the area of the intersection of the two circles?

(A) $\frac{1}{2}\pi r^2$

(B) $(\frac{2\pi}{3} - \frac{\sqrt{3}}{2})r^2$

(C) $(\frac{\pi}{3} - \frac{\sqrt{3}}{4})r^2$

(D) $\frac{4\pi}{3}r^2$

Question 14. A floor is to be tiled with square tiles of side $15\ \text{cm}$. The room is $6\ \text{m}$ long and $4.5\ \text{m}$ wide. How many tiles are needed?

(A) 1200 tiles

(B) 1500 tiles

(C) 800 tiles

(D) 1600 tiles

Question 15. A circular track has an inner radius of $14\ \text{m}$ and an outer radius of $21\ \text{m}$. What is the area of the track? (Use $\pi = \frac{22}{7}$)

(A) $770\ \text{m}^2$

(B) $1540\ \text{m}^2$

(C) $308\ \text{m}^2$

(D) $1078\ \text{m}^2$

Question 16. The perimeter of the track described in Question 15 is the sum of the circumferences of the inner and outer circles. True or False?

(A) True

(B) False

(C) Depends on the width

(D) Only if the track is solid

Question 17. A square is inscribed in a circle of radius $r$. What is the area of the square?

(A) $r^2$

(B) $2r^2$

(C) $\frac{1}{2} r^2$

(D) $4r^2$

Question 18. A rectangle is inscribed in a circle of radius $5\ \text{cm}$. If the length of the rectangle is $8\ \text{cm}$, what is its area?

(A) $30\ \text{cm}^2$

(B) $40\ \text{cm}^2$

(C) $48\ \text{cm}^2$

(D) $64\ \text{cm}^2$

Question 19. A path is to be built along the boundary of a rectangular field $90\ \text{m}$ by $60\ \text{m}$. If the path is $3\ \text{m}$ wide outside the field, what is the area of the path?

(A) $900\ \text{m}^2$

(B) $1044\ \text{m}^2$

(C) $5400\ \text{m}^2$

(D) $6444\ \text{m}^2$

Question 20. A design is made by drawing semicircles on the diameters of the sides of an equilateral triangle. To find the area of the design, you would typically:

(A) Add the areas of the three semicircles.

(B) Subtract the area of the triangle from the sum of semicircle areas.

(C) Add the areas of the three semicircles and the area of the triangle.

(D) This is a complex problem requiring integration.

Question 1. Which of the following is NOT a two-dimensional shape?

(A) Square

(B) Circle

(C) Cube

(D) Triangle

Question 2. Solid shapes are also known as:

(A) Plane figures

(B) 2D shapes

(C) 3D shapes

(D) Linear shapes

Question 3. The flat surfaces of a solid figure are called its:

(A) Edges

(B) Vertices

(C) Faces

(D) Diagonals

Question 4. The line segments where two faces of a solid figure meet are called its:

(A) Vertices

(B) Edges

(C) Faces

(D) Corners

Question 5. The points where three or more edges of a solid figure meet are called its:

(A) Faces

(B) Edges

(C) Centres

(D) Vertices

Question 6. How many faces does a cube have?

(A) 4

(B) 6

(C) 8

(D) 12

Question 7. How many edges does a cube have?

(A) 6

(B) 8

(C) 10

(D) 12

Question 8. How many vertices does a cube have?

(A) 6

(B) 8

(C) 12

(D) 4

Question 9. A solid shape with a circular base and a pointed top is called a:

(A) Cylinder

(B) Sphere

(C) Cone

(D) Cube

Question 10. A solid shape with two parallel and congruent circular bases joined by a curved surface is called a:

(A) Cone

(B) Cylinder

(C) Sphere

(D) Prism

Question 11. A solid shape that is perfectly round, where every point on its surface is equidistant from the centre, is called a:

(A) Circle

(B) Hemisphere

(C) Sphere

(D) Cylinder

Question 12. A polyhedron is a solid figure whose faces are:

(A) Circles

(B) Curved surfaces

(C) Polygons

(D) Any closed shapes

Question 13. Which of the following is NOT a polyhedron?

(A) Cube

(B) Pyramid

(C) Cylinder

(D) Prism

Question 14. A solid shape with a polygonal base and triangular faces meeting at a common vertex is called a:

(A) Prism

(B) Pyramid

(C) Cylinder

(D) Cone

Question 15. A solid shape with two identical and parallel polygonal bases and rectangular (or parallelogram) faces joining the corresponding sides is called a:

(A) Pyramid

(B) Cone

(C) Prism

(D) Sphere

Question 16. A triangular prism has how many faces?

(A) 3

(B) 4

(C) 5

(D) 6

Question 17. A square pyramid has how many edges?

(A) 4

(B) 6

(C) 8

(D) 12

Question 18. The base of a cone is a:

(A) Square

(B) Triangle

(C) Circle

(D) Rectangle

Question 19. Euler's formula for polyhedrons relates the number of Faces (F), Vertices (V), and Edges (E). The formula is:

(A) $F + V = E + 2$

(B) $F + E = V + 2$

(C) $V + E = F + 2$

(D) $F + V + E = 2$

Question 20. Applying Euler's formula to a cube (F=6, V=8, E=12), which option is correct?

(A) $6+8 = 12+2$

(B) $6+12 = 8+2$

(C) $8+12 = 6+2$

(D) $6+8+12 = 2$

Question 1. Surface area of a solid is the sum of the areas of all its:

(A) Edges

(B) Vertices

(C) Faces (or curved surfaces)

(D) Volume

Question 2. The area of only the side faces of a prism or pyramid (excluding the bases) is called the:

(A) Total Surface Area (TSA)

(B) Lateral Surface Area (LSA)

(C) Curved Surface Area (CSA)

(D) Base Area

Question 3. For shapes with curved surfaces like cylinders and cones, the area of the curved part is often called the:

(A) Lateral Surface Area (LSA)

(B) Total Surface Area (TSA)

(C) Base Area

(D) Volume

Question 4. What is the Total Surface Area (TSA) of a cube with side length $a$?

(A) $a^3$

(B) $4a^2$

(C) $6a^2$

(D) $a^2$

Question 5. What is the Lateral Surface Area (LSA) of a cube with side length $a$?

(A) $6a^2$

(B) $4a^2$

(C) $a^3$

(D) $2a^2$

Question 6. A cuboid has length $l$, width $w$, and height $h$. What is its Total Surface Area (TSA)?

(A) $lwh$

(B) $2(lw + wh + hl)$

(C) $lw + wh + hl$

(D) $2(l+w)h$

Question 7. What is the Lateral Surface Area (LSA) of a cuboid with length $l$, width $w$, and height $h$?

(A) $2(lw + wh + hl)$

(B) $lwh$

(C) $2(l+w)h$

(D) $lw + wh + hl - lw$

Question 8. A cylindrical pillar has a radius of $20\ \text{cm}$ and a height of $7\ \text{m}$. What is its Curved Surface Area (CSA)? (Use $\pi = \frac{22}{7}$ and convert units)

(A) $8.8\ \text{m}^2$

(B) $17.6\ \text{m}^2$

(C) $88\ \text{m}^2$

(D) $176\ \text{m}^2$

Question 9. What is the Total Surface Area (TSA) of a solid cylinder with radius $r$ and height $h$?

(A) $2\pi r h$

(B) $\pi r^2 h$

(C) $2\pi r(r+h)$

(D) $2\pi r^2 + h$

Question 10. The base radius of a cone is $r$ and its slant height is $l$. What is its Curved Surface Area (CSA)?

(A) $\pi r l$

(B) $\pi r^2 h$

(C) $\pi r^2 + \pi r l$

(D) $\frac{1}{3}\pi r^2 h$

Question 11. The Total Surface Area (TSA) of a solid cone with base radius $r$ and slant height $l$ is:

(A) $\pi r l$

(B) $\pi r^2 + \pi r l$

(C) $\frac{1}{3}\pi r^2 h$

(D) $2\pi r$

Question 12. What is the surface area of a sphere with radius $r$?

(A) $\frac{4}{3}\pi r^3$

(B) $2\pi r^2$

(C) $3\pi r^2$

(D) $4\pi r^2$

Question 13. What is the Curved Surface Area (CSA) of a hemisphere with radius $r$?

(A) $4\pi r^2$

(B) $2\pi r^2$

(C) $3\pi r^2$

(D) $\frac{2}{3}\pi r^3$

Question 14. What is the Total Surface Area (TSA) of a solid hemisphere with radius $r$?

(A) $2\pi r^2$

(B) $\pi r^2$

(C) $3\pi r^2$

(D) $4\pi r^2$

Question 15. A cubical tank has a side length of $1.5\ \text{m}$. It is to be painted on the outside, except for the bottom. What is the area to be painted?

(A) $13.5\ \text{m}^2$

(B) $9\ \text{m}^2$

(C) $11.25\ \text{m}^2$

(D) $6.75\ \text{m}^2$

Question 16. A rectangular box is $30\ \text{cm}$ long, $20\ \text{cm}$ wide, and $10\ \text{cm}$ high. What is its TSA?

(A) $600\ \text{cm}^2$

(B) $1100\ \text{cm}^2$

(C) $2200\ \text{cm}^2$

(D) $3300\ \text{cm}^2$

Question 17. A cylinder has base radius $7\ \text{cm}$ and height $10\ \text{cm}$. What is its CSA? (Use $\pi = \frac{22}{7}$)

(A) $220\ \text{cm}^2$

(B) $440\ \text{cm}^2$

(C) $660\ \text{cm}^2$

(D) $880\ \text{cm}^2$

Question 18. A cone has base radius $7\ \text{cm}$ and height $24\ \text{cm}$. What is its slant height?

(A) $25\ \text{cm}$

(B) $31\ \text{cm}$

(C) $38\ \text{cm}$

(D) $50\ \text{cm}$

Question 19. What is the CSA of the cone described in Question 18? (Use $\pi = \frac{22}{7}$)

(A) $550\ \text{cm}^2$

(B) $704\ \text{cm}^2$

(C) $1254\ \text{cm}^2$

(D) $1408\ \text{cm}^2$

Question 20. A sphere has a radius of $21\ \text{cm}$. What is its surface area? (Use $\pi = \frac{22}{7}$)

(A) $1386\ \text{cm}^2$

(B) $5544\ \text{cm}^2$

(C) $2772\ \text{cm}^2$

(D) $11088\ \text{cm}^2$

Question 1. Volume of a solid refers to the amount of:

(A) Surface area it covers

(B) Space it occupies

(C) Boundary length it has

(D) Flat surfaces it has

Question 2. The standard unit for measuring volume is:

(A) Square metre ($\text{m}^2$)

(B) Metre ($\text{m}$)

(C) Cubic metre ($\text{m}^3$)

(D) Hectare ($\text{ha}$)

Question 3. What is the volume of a cube with side length $a$?

(A) $6a^2$

(B) $4a^2$

(C) $a^3$

(D) $3a$

Question 4. What is the volume of a cuboid with length $l$, width $w$, and height $h$?

(A) $2(lw+wh+hl)$

(B) $lwh$

(C) $l+w+h$

(D) $Area_{base} + h$

Question 5. A cubical tank has a side length of $2\ \text{m}$. What is the volume of water it can hold?

(A) $4\ \text{m}^3$

(B) $6\ \text{m}^3$

(C) $8\ \text{m}^3$

(D) $12\ \text{m}^3$

Question 6. A rectangular tank is $5\ \text{m}$ long, $3\ \text{m}$ wide, and $2\ \text{m}$ deep. What is its volume?

(A) $10\ \text{m}^3$

(B) $15\ \text{m}^3$

(C) $30\ \text{m}^3$

(D) $60\ \text{m}^3$

Question 7. What is the volume of a cylinder with base radius $r$ and height $h$?

(A) $2\pi r h$

(B) $\pi r^2 h$

(C) $2\pi r(r+h)$

(D) $\frac{1}{3}\pi r^2 h$

Question 8. A cylindrical water tank has a base diameter of $14\ \text{m}$ and a height of $5\ \text{m}$. What is its volume? (Use $\pi = \frac{22}{7}$)

(A) $154\ \text{m}^3$

(B) $308\ \text{m}^3$

(C) $770\ \text{m}^3$

(D) $1540\ \text{m}^3$

Question 9. What is the volume of a cone with base radius $r$ and height $h$?

(A) $\pi r^2 h$

(B) $2\pi r h$

(C) $\frac{1}{3}\pi r^2 h$

(D) $\frac{4}{3}\pi r^3$

Question 10. A cone has a base radius of $6\ \text{cm}$ and a height of $7\ \text{cm}$. What is its volume? (Use $\pi = \frac{22}{7}$)

(A) $132\ \text{cm}^3$

(B) $264\ \text{cm}^3$

(C) $792\ \text{cm}^3$

(D) $1584\ \text{cm}^3$

Question 11. What is the volume of a sphere with radius $r$?

(A) $4\pi r^2$

(B) $2\pi r^2$

(C) $\frac{4}{3}\pi r^3$

(D) $\frac{2}{3}\pi r^3$

Question 12. What is the volume of a hemisphere with radius $r$?

(A) $\frac{4}{3}\pi r^3$

(B) $\frac{2}{3}\pi r^3$

(C) $2\pi r^2$

(D) $3\pi r^2$

Question 13. A metallic sphere of radius $4.2\ \text{cm}$ is melted. What is its volume? (Use $\pi = \frac{22}{7}$)

(A) $98.784\ \text{cm}^3$

(B) $310.464\ \text{cm}^3$

(C) $38.808\ \text{cm}^3$

(D) $248.384\ \text{cm}^3$

Question 14. The volume of a cylinder is $V = \pi r^2 h$. If the radius is doubled and the height is halved, how does the volume change?

(A) Volume is doubled

(B) Volume is halved

(C) Volume becomes four times

(D) Volume remains the same

Question 15. A solid metallic cuboid of dimensions $9\ \text{cm} \times 8\ \text{cm} \times 2\ \text{cm}$ is melted and recast into a cube. What is the side length of the new cube?

(A) $4\ \text{cm}$

(B) $5\ \text{cm}$

(C) $6\ \text{cm}$

(D) $7\ \text{cm}$

Question 16. The ratio of the volumes of two spheres is $8:27$. What is the ratio of their radii?

(A) $2:3$

(B) $4:9$

(C) $8:27$

(D) $\sqrt{8}:\sqrt{27}$

Question 17. The volume of a cylinder is $3080\ \text{cm}^3$ and its height is $20\ \text{cm}$. What is the radius of its base? (Use $\pi = \frac{22}{7}$)

(A) $7\ \text{cm}$

(B) $14\ \text{cm}$

(C) $21\ \text{cm}$

(D) $28\ \text{cm}$

Question 18. A cone and a cylinder have the same base radius and height. If the volume of the cylinder is $300\ \text{cm}^3$, what is the volume of the cone?

(A) $100\ \text{cm}^3$

(B) $300\ \text{cm}^3$

(C) $900\ \text{cm}^3$

(D) $150\ \text{cm}^3$

Question 19. How many litres of water can a hemispherical tank of radius $1.4\ \text{m}$ hold? ($1\ \text{m}^3 = 1000$ litres) (Use $\pi = \frac{22}{7}$)

(A) 4.1064 litres

(B) 4106.4 litres

(C) 5.7496 litres

(D) 5749.6 litres

Question 20. A solid sphere of radius $3\ \text{cm}$ is melted and recast into smaller spherical balls of radius $0.6\ \text{cm}$. How many small balls are formed?

(A) 5

(B) 25

(C) 50

(D) 125

Question 1. When two solids are combined, how is the total surface area of the new solid usually calculated?

(A) Sum of the total surface areas of the individual solids.

(B) Sum of the total surface areas of the individual solids minus the area of the joint surface(s).

(C) Sum of the curved surface areas of the individual solids.

(D) Multiply the volumes of the individual solids.

Question 2. When two solids are combined, how is the total volume of the new solid usually calculated?

(A) Sum of the volumes of the individual solids.

(B) Sum of the volumes of the individual solids minus the volume of the joint part.

(C) Average of the volumes of the individual solids.

(D) Product of the volumes of the individual solids.

Question 3. A toy is in the form of a cone mounted on a hemisphere. The diameter of the base of the cone is $7\ \text{cm}$ and the height of the cone is $10\ \text{cm}$. What is the radius of the hemisphere?

(A) $3.5\ \text{cm}$

(B) $7\ \text{cm}$

(C) $10\ \text{cm}$

(D) $5\ \text{cm}$

Question 4. For the toy in Question 3, what surfaces contribute to the total surface area of the toy?

(A) CSA of cone + Base area of cone + CSA of hemisphere

(B) TSA of cone + TSA of hemisphere

(C) CSA of cone + CSA of hemisphere

(D) CSA of cone + CSA of hemisphere + Base area of hemisphere

Question 5. A metallic cylinder has a height of $20\ \text{cm}$ and a base diameter of $14\ \text{cm}$. A cone of the same base radius is removed from the top. If the height of the cone is $12\ \text{cm}$, what is the volume of the remaining solid? (Use $\pi = \frac{22}{7}$)

(A) Volume of cylinder $+$ Volume of cone

(B) Volume of cylinder $-$ Volume of cone

(C) $\frac{1}{3}$ Volume of cylinder

(D) Volume of cylinder $-$ Area of cone base

Question 6. Calculate the volume of the remaining solid in Question 5.

(A) $3080\ \text{cm}^3$

(B) $550\ \text{cm}^3$

(C) $2530\ \text{cm}^3$

(D) $3630\ \text{cm}^3$

Question 7. A decorative block is made of a cube of side $5\ \text{cm}$ topped by a hemisphere of radius $2.1\ \text{cm}$. To find the total surface area, you would sum the TSA of the cube and TSA of the hemisphere and subtract twice the base area of the hemisphere. Why?

(A) The hemisphere covers a part of the cube's top face.

(B) The base of the hemisphere is hidden.

(C) This formula is always used for combined solids.

(D) The cube's base is also hidden.

Question 8. A solid is in the shape of a cone standing on a hemisphere, both with radius $1\ \text{cm}$ and the height of the cone is equal to its radius. What is the volume of the solid? (Use $\pi = \frac{22}{7}$)

(A) $\pi\ \text{cm}^3$

(B) $\frac{2\pi}{3}\ \text{cm}^3$

(C) $\frac{1\pi}{3}\ \text{cm}^3$

(D) $2\pi\ \text{cm}^3$

Question 9. A cylindrical vessel with internal diameter $10\ \text{cm}$ and height $10.5\ \text{cm}$ is full of water. A solid cone of base diameter $7\ \text{cm}$ and height $6\ \text{cm}$ is placed in it. The volume of water displaced is equal to the volume of the cone. True or False?

(A) True

(B) False

(C) Only if the cone is fully submerged

(D) Only if the cone floats

Question 10. Calculate the volume of water displaced in Question 9. (Use $\pi = \frac{22}{7}$)

(A) $77\ \text{cm}^3$

(B) $154\ \text{cm}^3$

(C) $308\ \text{cm}^3$

(D) $550\ \text{cm}^3$

Question 11. If a hemisphere is removed from one end of a cylinder, the remaining solid's volume is the volume of the cylinder minus the volume of the hemisphere. True or False?

(A) True

(B) False

(C) Only if the hemisphere's radius equals the cylinder's radius

(D) Only if the height of the cylinder is sufficient

Question 12. A tent is in the shape of a cylinder surmounted by a conical top. The height and diameter of the cylindrical part are $2.1\ \text{m}$ and $4\ \text{m}$ respectively, and the slant height of the conical part is $2.8\ \text{m}$. What is the area of the canvas used for making the tent?

(A) Area of cylinder base + CSA of cylinder + CSA of cone

(B) CSA of cylinder + CSA of cone

(C) TSA of cylinder + TSA of cone

(D) CSA of cylinder + CSA of cone + Area of both bases

Question 13. Calculate the area of the canvas used in Question 12. (Use $\pi = \frac{22}{7}$)

(A) $34.4\ \text{m}^2$

(B) $44\ \text{m}^2$

(C) $54\ \text{m}^2$

(D) $64\ \text{m}^2$

Question 14. A solid is composed of a cylinder with hemispherical ends. The total height of the solid is $19\ \text{cm}$ and the diameter of the cylinder is $7\ \text{cm}$. What is the radius of the hemisphere?

(A) $3.5\ \text{cm}$

(B) $7\ \text{cm}$

(C) $19\ \text{cm}$

(D) $10.5\ \text{cm}$

Question 15. What is the height of the cylindrical part of the solid in Question 14?

(A) $19\ \text{cm}$

(B) $12\ \text{cm}$

(C) $15.5\ \text{cm}$

(D) $10.5\ \text{cm}$

Question 16. To find the total surface area of the solid in Question 14, you would sum:

(A) TSA of cylinder + TSA of two hemispheres

(B) CSA of cylinder + CSA of two hemispheres

(C) TSA of cylinder + CSA of two hemispheres

(D) CSA of cylinder + TSA of two hemispheres

Question 17. What is the volume of the solid described in Question 14? (Use $\pi = \frac{22}{7}$)

(A) Volume of cylinder + Volume of hemisphere

(B) Volume of cylinder + Volume of two hemispheres

(C) Volume of cylinder $-$ Volume of two hemispheres

(D) Volume of cylinder + Base area of cylinder

Question 18. Calculate the volume of the solid in Question 14.

(A) $462\ \text{cm}^3$

(B) $693\ \text{cm}^3$

(C) $924\ \text{cm}^3$

(D) $1155\ \text{cm}^3$

Question 19. A wooden article was made by scooping out a hemisphere from each end of a solid cylinder. If the height of the cylinder is $10\ \text{cm}$ and its base radius is $3.5\ \text{cm}$, what is the total surface area of the article?

(A) CSA of cylinder $+$ CSA of one hemisphere

(B) CSA of cylinder $+$ CSA of two hemispheres

(C) TSA of cylinder $-$ Area of two hemisphere bases

(D) TSA of cylinder $+$ Area of two hemisphere bases

Question 20. Calculate the total surface area of the article in Question 19. (Use $\pi = \frac{22}{7}$)

(A) $220\ \text{cm}^2$

(B) $330\ \text{cm}^2$

(C) $440\ \text{cm}^2$

(D) $550\ \text{cm}^2$

Question 1. When a solid is converted from one shape to another, which property remains conserved (assuming no material is wasted)?

(A) Surface Area

(B) Volume

(C) Height

(D) Radius

Question 2. A metallic sphere of radius $6\ \text{cm}$ is melted and recast into a cylinder of height $32\ \text{cm}$. What is the radius of the cylinder? (Use $\pi = \frac{22}{7}$)

(A) $3\ \text{cm}$

(B) $4\ \text{cm}$

(C) $4.5\ \text{cm}$

(D) $5\ \text{cm}$

Question 3. A $20\ \text{m}$ deep well with diameter $7\ \text{m}$ is dug and the earth taken out is evenly spread to form a platform $22\ \text{m}$ by $14\ \text{m}$. What is the height of the platform? (Use $\pi = \frac{22}{7}$)

(A) $1.5\ \text{m}$

(B) $2\ \text{m}$

(C) $2.5\ \text{m}$

(D) $3\ \text{m}$

Question 4. A cone is cut by a plane parallel to the base. The portion between the plane and the base is called a:

(A) Hemisphere

(B) Cylinder

(C) Frustum of a cone

(D) Sector

Question 5. A frustum of a cone has radii of circular bases $r_1$ and $r_2$ ($r_1 > r_2$) and height $h$. What is its volume?

(A) $\frac{1}{3}\pi h (r_1^2 + r_2^2 + r_1 r_2)$

(B) $\pi h (r_1^2 + r_2^2 + r_1 r_2)$

(C) $\frac{1}{3}\pi h (r_1 + r_2)^2$

(D) $\frac{1}{3}\pi h (r_1 - r_2)^2$

Question 6. A frustum of a cone has radii of circular bases $r_1$ and $r_2$ and slant height $l$. What is its curved surface area?

(A) $\pi (r_1 + r_2) l$

(B) $\pi l (r_1^2 + r_2^2)$

(C) $\pi (r_1 - r_2) l$

(D) $\pi l (r_1 + r_2) + \pi r_1^2 + \pi r_2^2$

Question 7. The radii of the ends of a frustum of a cone are $14\ \text{cm}$ and $6\ \text{cm}$ and its height is $6\ \text{cm}$. What is its slant height?

(A) $8\ \text{cm}$

(B) $10\ \text{cm}$

(C) $12\ \text{cm}$

(D) $14\ \text{cm}$

Question 8. What is the curved surface area of the frustum in Question 7? (Use $\pi = \frac{22}{7}$)

(A) $440\ \text{cm}^2$

(B) $628\ \text{cm}^2$

(C) $880\ \text{cm}^2$

(D) $1100\ \text{cm}^2$

Question 9. What is the volume of the frustum in Question 7? (Use $\pi = \frac{22}{7}$)

(A) $1088\ \text{cm}^3$

(B) $2200\ \text{cm}^3$

(C) $2928\ \text{cm}^3$

(D) $4400\ \text{cm}^3$

Question 10. The radii of the top and bottom of a bucket in the shape of a frustum of a cone are $10\ \text{cm}$ and $20\ \text{cm}$ respectively. If its height is $12\ \text{cm}$, what is its slant height?

(A) $10\ \text{cm}$

(B) $13\ \text{cm}$

(C) $15\ \text{cm}$

(D) $20\ \text{cm}$

Question 11. What is the capacity (volume) of the bucket in Question 10? (Use $\pi = \frac{22}{7}$)

(A) $1760\ \text{cm}^3$

(B) $8800\ \text{cm}^3$

(C) $17600\ \text{cm}^3$

(D) $22000/3\ \text{cm}^3$

Question 12. The total surface area of a frustum of a cone is given by:

(A) CSA + Area of top base + Area of bottom base

(B) CSA + Area of top base

(C) CSA + Area of bottom base

(D) CSA + Area of top base $\times$ Area of bottom base

Question 13. A solid cone is cut into two parts by a plane parallel to the base at a height of $1/3$rd of the height from the base. The ratio of the volume of the small cone to the volume of the frustum is:

(A) $1:3$

(B) $1:8$

(C) $1:26$

(D) $1:27$

Question 14. A spherical glass vessel has a cylindrical neck $8\ \text{cm}$ long, $2\ \text{cm}$ in diameter; the spherical part is $8.5\ \text{cm}$ in diameter. The amount of water it can hold is measured by finding its volume. True or False?

(A) True

(B) False

(C) Only if the neck is also full

(D) Only if the sphere is empty

Question 15. Calculate the volume of the glass vessel in Question 14. (Use $\pi = 3.14$)

(A) $346.5\ \text{cm}^3$

(B) $321.39\ \text{cm}^3$

(C) $321.39 + 25.12 = 346.51\ \text{cm}^3$ approx.

(D) $346.5\ \text{cm}^3$ approx.

Question 16. The radii of the ends of a metallic frustum bucket are $28\ \text{cm}$ and $7\ \text{cm}$. The height is $45\ \text{cm}$. The metal sheet used to make the bucket (excluding the handle) is:

(A) CSA of frustum

(B) TSA of frustum

(C) CSA of frustum + Area of bottom base

(D) CSA of frustum + Area of top base

Question 17. The height of a cone is $15\ \text{cm}$. If a small cone is cut off at the top by a plane parallel to the base, and its volume is $1/27$ of the volume of the original cone, at what height above the base was the section made?

(A) $5\ \text{cm}$

(B) $10\ \text{cm}$

(C) $12\ \text{cm}$

(D) $13\ \text{cm}$

Question 18. A solid right circular cone is cut into two parts at the middle of its height by a plane parallel to the base. The ratio of the volume of the lower part (frustum) to the volume of the upper part (cone) is:

(A) $1:7$

(B) $7:1$

(C) $1:8$

(D) $8:1$

Question 19. A solid consisting of a right circular cone of height $120\ \text{cm}$ and radius $60\ \text{cm}$ standing on a hemisphere of radius $60\ \text{cm}$ is placed upright in a right circular cylinder full of water such that it touches the bottom. The radius of the cylinder is $60\ \text{cm}$ and its height is $180\ \text{cm}$. What is the volume of water left in the cylinder?

(A) Volume of cylinder $-$ Volume of combined solid

(B) Volume of cylinder $+$ Volume of combined solid

(C) Volume of combined solid $-$ Volume of cylinder

(D) Volume of cylinder $-$ Volume of cone

Question 20. Calculate the volume of water left in the cylinder in Question 19. (Use $\pi = \frac{22}{7}$)

(A) $113142.86\ \text{cm}^3$ (approx)

(B) $339428.57\ \text{cm}^3$ (approx)

(C) $565714.28\ \text{cm}^3$ (approx)

(D) $791999.99\ \text{cm}^3$ (approx)