CBSE Class 10 Mathematics Surface Areas and Volumes MCQs Set J

Question. The number of spherical bullets that can be made out of a solid cube of lead whose edge measures \( 88 \text{ cm} \), each bullet being \( 4 \text{ cm} \) in diameter, is
(a) \( 25000 \)
(b) \( 25440 \)
(c) \( 20328 \)
(d) \( 25140 \)
Answer: C

Question. The height of a conical tent is \( 14 \text{ m} \) and its floor area is \( 346.5 \text{ m}^2 \). The length of canvas, \( 1.1 \text{ m} \) wide, required for it is
(a) \( 490 \text{ m} \)
(b) \( 525 \text{ m} \)
(c) \( 665 \text{ m} \)
(d) \( 860 \text{ m} \)
Answer: B

Question. A solid metallic sphere of diameter \( 21 \text{ cm} \) is melted and recast into a number of smaller cones, each of diameter \( 3.5 \text{ cm} \), height \( 3 \text{ cm} \). The number of cones so formed is
(a) \( 405 \)
(b) \( 540 \)
(c) \( 504 \)
(d) none of these
Answer: C

Question. A metal sheet \( 27 \text{ cm} \) long, \( 8 \text{ cm} \) broad and \( 1 \text{ cm} \) thick is melted into a cube. The difference between surface areas of two solids is
(a) \( 284 \text{ cm}^2 \)
(b) \( 285 \text{ cm}^2 \)
(c) \( 286 \text{ cm}^2 \)
(d) \( 287 \text{ cm}^2 \)
Answer: C

Question. The curved surface area of a cylinder is \( 264 \text{ m}^2 \) and its volume is \( 924 \text{ m}^3 \). The ratio of its diameter to its height is
(a) \( 3 : 7 \)
(b) \( 7 : 3 \)
(c) \( 6 : 7 \)
(d) \( 7 : 6 \)
Answer: B

Question. The radius of spherical balloon increases from \( 8 \text{ cm} \) to \( 12 \text{ cm} \). The ratio of the surface areas of the balloon in two cases is
(a) \( 2 : 3 \)
(b) \( 3 : 2 \)
(c) \( 8 : 27 \)
(d) \( 4 : 9 \)
Answer: D

Question. If two cubes, each of edge \( 4 \text{ cm} \) are joined end to end, then the surface area of the resulting cuboid is
(a) \( 100 \text{ cm}^2 \)
(b) \( 160 \text{ cm}^2 \)
(c) \( 200 \text{ cm}^2 \)
(d) \( 80 \text{ cm}^2 \)
Answer: B

Question. A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is \( 16 \text{ cm} \) and the diameter of the cylinder is \( 7 \text{ cm} \). Then the total surface area of the solid is
(a) \( 324 \text{ cm}^2 \)
(b) \( 464 \text{ cm}^2 \)
(c) \( 418 \text{ cm}^2 \)
(d) \( 352 \text{ cm}^2 \)
Answer: D

Question. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is \( 42 \text{ cm} \) and the total height of the vessel is \( 30 \text{ cm} \). Find the inner surface area of the vessel.
(a) \( 3500 \text{ cm}^2 \)
(b) \( 3800 \text{ cm}^2 \)
(c) \( 3960 \text{ cm}^2 \)
(d) \( 3900 \text{ cm}^2 \)
Answer: C

Question. A solid is hemispherical at the bottom and conical above. If the surface areas of the two parts are equal, then the ratio of its radius and the height of its conical part is
(a) \( 1 : 3 \)
(b) \( 1 : \sqrt{3} \)
(c) \( 1 : 1 \)
(d) \( \sqrt{3} : 1 \)
Answer: B

Question. The volume of the largest right circular cone that can be cut out from a cube of edge \( 4.2 \text{ cm} \) is
(a) \( 9.7 \text{ cm}^3 \)
(b) \( 72.6 \text{ cm}^3 \)
(c) \( 58.2 \text{ cm}^3 \)
(d) \( 19.4 \text{ cm}^3 \)
Answer: D

Question. The volume of the largest right circular cone that can be carved out of a solid hemisphere of radius \( r \) is
(a) \( \frac{4}{3}\pi r^3 \)
(b) \( \frac{2}{3}\pi r^3 \)
(c) \( 4\pi r^2 \)
(d) \( \frac{1}{3}\pi r^3 \)
Answer: D

Question. If a cone is cut into two parts by a horizontal plane passing through the mid-point of its axis, then the ratio of the volume of the smaller cone to the whole cone is
(a) \( 1 : 2 \)
(b) \( 1 : 4 \)
(c) \( 1 : 6 \)
(d) \( 1 : 8 \)
Answer: D

Question. How many spherical lead shots each \( 4.2 \text{ cm} \) in diameter can be obtained from a solid cuboid with dimensions \( 66 \text{ cm}, 42 \text{ cm} \) and \( 21 \text{ cm} \)?
(a) \( 1500 \)
(b) \( 750 \)
(c) \( 500 \)
(d) \( 2000 \)
Answer: A

Question. The number of solid spheres, each of diameter \( 6 \text{ cm} \) that could be moulded to form a solid metal cylinder of height \( 54 \text{ cm} \) and diameter \( 4 \text{ cm} \), is
(a) \( 3 \)
(b) \( 4 \)
(c) \( 5 \)
(d) \( 6 \)
Answer: D

Question. Eight solid spheres of the same size are made by melting a solid metallic cylinder of base diameter \( 6 \text{ cm} \) and height \( 32 \text{ cm} \). The diameter of each sphere is
(a) \( 3 \text{ cm} \)
(b) \( 6 \text{ cm} \)
(c) \( 12 \text{ cm} \)
(d) \( 8 \text{ cm} \)
Answer: B

Question. The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is \( 8 \text{ cm} \), then height of the cone is
(a) \( 10 \text{ cm} \)
(b) \( 15 \text{ cm} \)
(c) \( 18 \text{ cm} \)
(d) \( 24 \text{ cm} \)
Answer: D

Question. A hollow cylinder of height \( 15 \text{ cm} \) is melted and cast into a solid cylinder of height \( 3 \text{ cm} \). If the internal and external radii of the hollow cylinder are \( 2 \text{ cm} \) and \( 3 \text{ cm} \) respectively, then the radius of the solid cylinder is
(a) \( 1 \text{ cm} \)
(b) \( 5 \text{ cm} \)
(c) \( 3 \text{ cm} \)
(d) \( 4 \text{ cm} \)
Answer: B

Assertion & Reasoning Based MCQs

Directions (53 to 60) : In these questions, a statement of Assertion is followed by a statement of Reason is given.
Choose the correct answer out of the following choices :
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.

Question. Assertion : A well of diameter \( 4 \text{ m} \) is dug \( 14 \text{ m} \) deep. The earth taken out of it has been spread evenly all around it to a width of \( 2 \text{ m} \) to form an embankment. Then the height of the embankment is \( 4\frac{2}{3} \text{ m} \).
Reason : Volume of cylinder \( = \pi r^2 h \), where \( h \) is height and \( r \) is the radius of the cylinder.
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.
Answer: A

Question. Assertion : The curved surface area of a cone of base radius \( 6 \text{ cm} \) and height \( 8 \text{ cm} \) is \( 60\pi \text{ cm}^2 \).
Reason : Curved surface area of a cone \( = \pi r^2 h \), where \( r \) be the radius and \( h \) be the height of cone.
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.
Answer: C

Question. Assertion : The slant height of the frustum of a cone is \( 4 \text{ cm} \) and the perimeters of its circular ends are \( 18 \text{ cm} \) and \( 6 \text{ cm} \). Then, the curved surface area of the frustum is \( 48 \text{ cm}^2 \).
Reason : If the radii of the circular ends of the frustum of a cone are \( r_1 \) and \( r_2 \) respectively and its height is \( h \), then its curved surface area is \( \pi(r_1 + r_2)l \), where \( l^2 = h^2 + (r_1 - r_2)^2 \).
(a) Assertion and Reason both are correct statements and Reason is the correct explanation of Assertion.
(b) Assertion and Reason both are correct statements but Reason is not the correct explanation of Assertion.
(c) Assertion is correct statement but Reason is wrong statement.
(d) Assertion is wrong statement but Reason is correct statement.
Answer: C