Assertion-Reason MCQs for Sub-Topics of Topic 7: Mensuration

Question 1. Assertion (A): Perimeter is a one-dimensional measurement.

Reason (R): Perimeter is the total length of the boundary of a two-dimensional figure.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 2. Assertion (A): Area is measured in square units like $\text{m}^2$ or $\text{cm}^2$.

Reason (R): Area measures the amount of surface enclosed by a two-dimensional figure.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 3. Assertion (A): Mensuration is the branch of mathematics that deals with the study of geometric shapes.

Reason (R): Mensuration specifically focuses on the measurement of length, area, and volume of geometric figures.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 4. Assertion (A): The perimeter of any actual physical closed figure must be a positive value.

Reason (R): Length measurements are always positive.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 5. Assertion (A): Calculating the amount of land in a farm involves finding its area.

Reason (R): Area measures the extent of a surface within a boundary.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 1. Assertion (A): The perimeter of a rectangle with length $l$ and width $w$ is $2(l+w)$.

Reason (R): A rectangle has two sides of length $l$ and two sides of width $w$, and perimeter is the sum of side lengths.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 2. Assertion (A): If the side length of a square is doubled, its perimeter is also doubled.

Reason (R): The perimeter of a square is directly proportional to its side length ($P=4s$).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 3. Assertion (A): The perimeter of any polygon is found by summing the lengths of all its sides.

Reason (R): A polygon is a closed figure formed by line segments, and the perimeter is the length of the boundary.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 4. Assertion (A): If a square and a rectangle have the same perimeter, they must have the same area.

Reason (R): Perimeter and area are distinct measurements and having the same perimeter does not guarantee the same area.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 5. Assertion (A): The perimeter of a triangle with side lengths 4 cm, 5 cm, and 10 cm is 19 cm.

Reason (R): The sum of any two sides of a triangle must be greater than the third side, and $4 + 5$ is not greater than $10$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 1. Assertion (A): The area of a triangle with base $b$ and height $h$ is $\frac{1}{2} \times b \times h$.

Reason (R): A triangle can be seen as half of a parallelogram that has the same base and is between the same parallel lines.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 2. Assertion (A): If the side of a square is $s$, its area is $s^2$.

Reason (R): Area is the product of length and width, and for a square, length and width are equal to the side length.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 3. Assertion (A): If a triangle and a parallelogram stand on the same base and between the same parallel lines, the area of the triangle is equal to the area of the parallelogram.

Reason (R): The area of a triangle is half the area of a parallelogram when they share the same base and lie between the same parallel lines.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 4. Assertion (A): The area of a square with diagonal $d$ is $\frac{d^2}{2}$.

Reason (R): In a square with diagonal $d$, the side length $s = \frac{d}{\sqrt{2}}$, and the area is $s^2$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 5. Assertion (A): The area of a trapezium with parallel sides $a$ and $b$ and height $h$ is $\frac{1}{2}(a+b)h$.

Reason (R): A trapezium can be divided into a rectangle and one or two triangles, and its area is the sum of the areas of these parts.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 1. Assertion (A): Heron's formula can be used to calculate the area of any triangle.

Reason (R): Heron's formula requires knowing the lengths of all three sides of the triangle.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 2. Assertion (A): For a triangle with sides $a, b, c$, the semi-perimeter $s = \frac{a+b+c}{2}$.

Reason (R): The semi-perimeter is defined as half of the perimeter of the triangle.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 3. Assertion (A): Heron's formula is $\sqrt{s(s-a)(s-b)(s-c)}$.

Reason (R): This formula calculates the area of a triangle using its semi-perimeter and side lengths.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 4. Assertion (A): For a triangle with sides 6 cm, 8 cm, and 10 cm, the area calculated by Heron's formula is equal to the area calculated by $\frac{1}{2} \times \text{base} \times \text{height}$.

Reason (R): The triangle with sides 6, 8, 10 cm is a right-angled triangle, and both formulas correctly calculate the area of any triangle.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 5. Assertion (A): If for a triangle with sides $a, b, c$, $s-a$, $s-b$, or $s-c$ is zero, the area is zero.

Reason (R): If $s-a=0$, then $s=a$, meaning $(a+b+c)/2 = a$, which gives $b+c=a$, a degenerate triangle.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 1. Assertion (A): The area of a rhombus with diagonals $d_1$ and $d_2$ is $\frac{1}{2}d_1 d_2$.

Reason (R): The diagonals of a rhombus intersect at right angles and divide the rhombus into four congruent right-angled triangles.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 2. Assertion (A): The area of a kite with diagonals $d_1$ and $d_2$ is $\frac{1}{2}d_1 d_2$.

Reason (R): The diagonals of a kite are perpendicular to each other.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 3. Assertion (A): The area of any quadrilateral can be found by dividing it into two triangles using a diagonal and summing their areas.

Reason (R): The area of a composite figure is the sum of the areas of its non-overlapping parts.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 4. Assertion (A): For a regular hexagon with side $s$, its area is $6 \times \frac{\sqrt{3}}{4}s^2$.

Reason (R): A regular hexagon can be divided into 6 congruent equilateral triangles with side length equal to the side length of the hexagon.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 5. Assertion (A): The formula for the area of a general quadrilateral with a diagonal $d$ and perpendiculars from opposite vertices $h_1$ and $h_2$ is $\frac{1}{2}d(h_1+h_2)$.

Reason (R): The diagonal splits the quadrilateral into two triangles with base $d$ and heights $h_1$ and $h_2$, and the area of a triangle is $\frac{1}{2} \times \text{base} \times \text{height}$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 1. Assertion (A): The circumference of a circle is $2\pi r$, where $r$ is the radius.

Reason (R): $\pi$ is defined as the ratio of the circumference of a circle to its diameter.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 2. Assertion (A): If the radius of a circle is doubled, its area becomes four times the original area.

Reason (R): The area of a circle is directly proportional to the square of its radius ($A=\pi r^2$).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 3. Assertion (A): The unit of circumference is the same as the unit of length, like metres or centimetres.

Reason (R): Circumference is a measure of the boundary length of the circle.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 4. Assertion (A): If the circumference of a circle is numerically equal to its area, then the radius of the circle is 2 units.

Reason (R): The equation $2\pi r = \pi r^2$ is obtained by equating the formulas for circumference and area, and its positive solution is $r=2$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 5. Assertion (A): The value of $\pi$ is exactly $\frac{22}{7}$.

Reason (R): $\frac{22}{7}$ is a rational number, while $\pi$ is an irrational number, so they cannot be exactly equal.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 1. Assertion (A): A sector of a circle is the region bounded by two radii and an arc.

Reason (R): A segment of a circle is the region bounded by a chord and an arc.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 2. Assertion (A): The area of a sector with central angle $\theta$ (in degrees) and radius $r$ is given by the formula $\frac{\theta}{360} \times \pi r^2$.

Reason (R): The area of a sector is proportional to the central angle subtended by the arc at the center.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 3. Assertion (A): The length of an arc of a sector with radius $r$ and central angle $\theta$ (in radians) is $r\theta$.

Reason (R): Arc length is directly proportional to both the radius of the circle and the central angle (in radians).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 4. Assertion (A): The area of a minor segment of a circle is found by subtracting the area of the triangle formed by the radii and the chord from the area of the corresponding sector.

Reason (R): The sector is composed of the triangle and the segment.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 5. Assertion (A): A semicircle is a sector of a circle with a central angle of $180^\circ$.

Reason (R): A straight angle at the center of a circle measures $180^\circ$ and forms a boundary along a diameter.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 1. Assertion (A): The area of a composite figure formed by combining non-overlapping basic shapes is the sum of the areas of the individual shapes.

Reason (R): Area is an additive property for distinct regions in a plane.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 2. Assertion (A): To find the perimeter of a composite figure, one must add the perimeters of all the individual shapes that form it.

Reason (R): The perimeter of a figure is the length of its outer boundary, and internal lines are not part of the perimeter.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 3. Assertion (A): The area of a path around a rectangular garden is found by subtracting the area of the garden from the area of the rectangle including the path.

Reason (R): The path is the region between the outer boundary (park + path) and the inner boundary (park).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 4. Assertion (A): If two squares are joined along one side, the area of the resulting composite figure is the sum of the areas of the two squares.

Reason (R): The two squares do not overlap when joined along a side, and area is additive for non-overlapping regions.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 5. Assertion (A): The perimeter of a shape made by cutting a circular hole in the center of a square is the sum of the perimeter of the square and the circumference of the circle.

Reason (R): The perimeter of a composite figure includes the length of all its outer boundaries.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 1. Assertion (A): A cube is a three-dimensional shape.

Reason (R): A cube has length, width, and height.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 2. Assertion (A): The faces of a polyhedron are always polygons.

Reason (R): A polyhedron is a solid figure bounded by flat surfaces, which are called faces, and these faces are polygonal in shape.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 3. Assertion (A): A sphere is an example of a polyhedron.

Reason (R): A sphere has a curved surface and does not have flat polygonal faces.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 4. Assertion (A): Euler's formula $F + V - E = 2$ applies to cubes, prisms, and pyramids.

Reason (R): Euler's formula is applicable to all polyhedrons.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 5. Assertion (A): A cylinder has edges and vertices.

Reason (R): Edges are formed where surfaces meet, and vertices are points where edges meet; a cylinder has a curved surface joining two flat bases.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 1. Assertion (A): Surface area of a solid is the sum of the areas of all its faces (and curved surfaces).

Reason (R): The surface of a solid is a two-dimensional boundary enclosing the solid.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 2. Assertion (A): The total surface area (TSA) of a solid cylinder with radius $r$ and height $h$ is $2\pi rh$.

Reason (R): $2\pi rh$ is the formula for the curved surface area (CSA) of a cylinder, and TSA includes the areas of the two bases as well.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 3. Assertion (A): The lateral surface area (LSA) of a cuboid is $2(l+w)h$, where $l, w, h$ are length, width, and height.

Reason (R): The LSA of a cuboid is the sum of the areas of its four side faces, which form a rectangle with length $2(l+w)$ and height $h$ when unrolled.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 4. Assertion (A): The surface area of a sphere with radius $r$ is $4\pi r^2$.

Reason (R): The surface area of a sphere is four times the area of a circle with the same radius.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 5. Assertion (A): The total surface area of a solid hemisphere of radius $r$ is $3\pi r^2$.

Reason (R): A solid hemisphere has a curved surface area of $2\pi r^2$ and a flat circular base area of $\pi r^2$, and its TSA is the sum of these two areas.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 1. Assertion (A): Volume is a measure of the space occupied by a three-dimensional solid.

Reason (R): A three-dimensional solid extends in three mutually perpendicular directions (length, width, and height).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 2. Assertion (A): The volume of a cylinder with base radius $r$ and height $h$ is $\pi r^2 h$.

Reason (R): The volume of any prism (including a cylinder) is the area of its base multiplied by its height.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 3. Assertion (A): The volume of a cone with base radius $r$ and height $h$ is $\frac{1}{3}\pi r^2 h$.

Reason (R): A cone can be inscribed within a cylinder of the same base and height, and the cone's volume is one-third of the cylinder's volume.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 4. Assertion (A): If the radius of a sphere is halved, its volume becomes one-fourth of the original volume.

Reason (R): The formula for the volume of a sphere is $V = \frac{4}{3}\pi r^3$, which shows volume is proportional to the cube of the radius.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 5. Assertion (A): 1 litre is equal to 1000 cubic centimetres ($1\ \text{L} = 1000\ \text{cm}^3$).

Reason (R): $1\ \text{m}^3$ is equal to 1000 litres, and $1\ \text{m}^3 = 1,000,000\ \text{cm}^3$, thus $1000\ \text{L} = 1,000,000\ \text{cm}^3$, which simplifies to $1\ \text{L} = 1000\ \text{cm}^3$.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 1. Assertion (A): When two basic solids are joined together, the total volume of the resulting solid is the sum of the volumes of the individual solids.

Reason (R): Volume is an additive property for solids that do not overlap.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 2. Assertion (A): To find the total surface area of a solid formed by joining a cone and a hemisphere on the same base, you sum the TSA of the cone and the TSA of the hemisphere.

Reason (R): The area of the common base between the cone and the hemisphere is an internal surface and is not part of the total surface area of the combined solid.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 3. Assertion (A): If a solid is formed by scooping out a hemisphere from one end of a cylinder, the volume of the remaining solid is the volume of the cylinder minus the volume of the hemisphere.

Reason (R): The volume of a removed part is subtracted from the volume of the original solid to find the volume of the remaining part.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 4. Assertion (A): When a solid object is fully submerged in a liquid in a cylindrical container, the volume of liquid that rises is equal to the volume of the object.

Reason (R): The volume of the displaced liquid is equal to the volume of the submerged part of the object.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 5. Assertion (A): The total surface area of a solid formed by placing a cube on the ground and a hemisphere on its top face (same radius/half side) includes the area of the base of the hemisphere.

Reason (R): The base of the hemisphere is covered by the top face of the cube and is not exposed to the outside.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 1. Assertion (A): When a solid metallic sphere is melted and recast into a cylinder, the volume of the cylinder is equal to the volume of the sphere.

Reason (R): The volume of the material is conserved when a solid is converted from one shape to another, assuming no loss.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 2. Assertion (A): The earth dug out from a cylindrical well can be used to form a rectangular platform of the same volume.

Reason (R): The volume of the excavated material equals the volume of the space it occupied.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 3. Assertion (A): A frustum of a cone has two parallel circular bases of different radii.

Reason (R): A frustum is formed by cutting a cone by a plane parallel to its base and removing the smaller cone part.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 4. Assertion (A): The formula for the curved surface area of a frustum of a cone is $\pi (r_1 + r_2) l$, where $r_1$ and $r_2$ are the radii of the bases and $l$ is the slant height.

Reason (R): The lateral surface of a frustum can be unrolled into a part of a circular annulus (ring).

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.

Question 5. Assertion (A): A bucket, open at the top and in the shape of a frustum of a cone, requires metal sheet area equal to its CSA plus the area of its bottom base.

Reason (R): The bucket is open at the top, so the area of the top circular base is not covered by the metal sheet.

(A) Both A and R are true and R is the correct explanation of A.

(B) Both A and R are true but R is not the correct explanation of A.

(C) A is true but R is false.

(D) A is false but R is true.