CBSE Class 10 Surface Areas and Volumes Sure Shot Questions Set 03

Multiple Choice Questions 

Question. The volume of a cube is \( 2744 \text{ cm}^3 \). Its surface area is
(a) \( 196 \text{ cm}^2 \)
(b) \( 1176 \text{ cm}^2 \)
(c) \( 784 \text{ cm}^2 \)
(d) \( 588 \text{ cm}^2 \)
Answer: (b)

Question. The ratio of the total surface area to the lateral surface area of a cylinder with base radius \( 80 \text{ cm} \) and height \( 20 \text{ cm} \) is
(a) \( 1 : 2 \)
(b) \( 2 : 1 \)
(c) \( 3 : 1 \)
(d) \( 5 : 1 \)
Answer: (d)

Question. The height of a cylinder is \( 14 \text{ cm} \) and its curved surface area is \( 264 \text{ cm}^2 \). The volume of the cylinder is
(a) \( 296 \text{ cm}^3 \)
(b) \( 396 \text{ cm}^3 \)
(c) \( 369 \text{ cm}^3 \)
(d) \( 503 \text{ cm}^3 \)
Answer: (b)

Question. The ratio of the volumes of two spheres is \( 8 : 27 \). The ratio between their surface areas is
(a) \( 2 : 3 \)
(b) \( 4 : 27 \)
(c) \( 8 : 9 \)
(d) \( 4 : 9 \)
Answer: (d)

Question. The radii of the base of a cylinder and a cone are in the ratio \( 3 : 4 \) and their heights are in the ratio \( 2 : 3 \), then ratio of their volumes is
(a) \( 9 : 8 \)
(b) \( 9 : 4 \)
(c) \( 3 : 1 \)
(d) \( 27 : 64 \)
Answer: (a)

Question. The base radius of the cylinder is \( 1 \frac{2}{3} \) times its height. The cost of painting its C.S.A. at \( 2 \text{ paise/cm}^2 \) is \( Rs 92.40 \). The volume of the cylinder is
(a) \( 80850 \text{ cm}^3 \)
(b) \( 88850 \text{ cm}^3 \)
(c) \( 80508 \text{ cm}^3 \)
(d) none of these
Answer: (a)

Question. A spherical ball of radius \( 3 \text{ cm} \) is melted and recast into three spherical balls. The radii of two of these balls are \( 1.5 \text{ cm} \) and \( 2 \text{ cm} \). The radius of the third ball is
(a) \( 1.5 \text{ cm} \)
(b) \( 2 \text{ cm} \)
(c) \( 3 \text{ cm} \)
(d) \( 2.5 \text{ cm} \)
Answer: (d)

Question. A circus tent is cylindrical up to a height of \( 4 \text{ m} \) and conical above it. If its diameter is \( 105 \text{ m} \) and its slant height is \( 40 \text{ m} \), the total area of canvas required to built the tent is
(a) \( 7920 \text{ m}^2 \)
(b) \( 7820 \text{ m}^2 \)
(c) \( 9720 \text{ m}^2 \)
(d) \( 2645 \text{ m}^2 \)
Answer: (a)

Question. A glass cylinder with diameter \( 20 \text{ cm} \) has water to a height of \( 9 \text{ cm} \). A metal cube of \( 8 \text{ cm} \) edge is immersed in it completely. The height by which water will rise in the cylinder is (Take \( \pi = 3.14 \))
(a) \( 1.6 \text{ cm} \)
(b) \( 2.5 \text{ cm} \)
(c) \( 1 \text{ cm} \)
(d) \( 2.6 \text{ cm} \)
Answer: (a)

Question. The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is \( 5 \text{ cm} \), then height of the cone is
(a) \( 10 \text{ cm} \)
(b) \( 15 \text{ cm} \)
(c) \( 18 \text{ cm} \)
(d) \( 24 \text{ cm} \)
Answer: (b)

Question. A cylindrical vessel \( 16 \text{ cm} \) high and \( 9 \text{ cm} \) as the radius of the base, is filled with sand. This vessel is emptied on the ground and a conical heap of sand is formed. If the height of the conical heap is \( 12 \text{ cm} \), the radius of its base is
(a) \( 12 \text{ cm} \)
(b) \( 18 \text{ cm} \)
(c) \( 36 \text{ cm} \)
(d) \( 48 \text{ cm} \)
Answer: (b)

Question. The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius \( 1 \text{ cm} \) and height \( 5 \text{ cm} \) is
(a) \( \frac{4}{3} \pi \text{ cm}^3 \)
(b) \( \frac{10}{3} \pi \text{ cm}^3 \)
(c) \( 5\pi \text{ cm}^3 \)
(d) \( \frac{20}{3} \pi \text{ cm}^3 \)
Answer: (a)

Question. \( 12 \) spheres of the same size are made from melting a solid cylinder of \( 16 \text{ cm} \) diameter and \( 2 \text{ cm} \) height. The diameter of each sphere is
(a) \( \sqrt{3} \text{ cm} \)
(b) \( 2 \text{ cm} \)
(c) \( 3 \text{ cm} \)
(d) \( 4 \text{ cm} \)
Answer: (b)

Question. A rectangular sheet of paper \( 44 \text{ cm} \times 18 \text{ cm} \) is rolled along its length and a cylinder is formed. The volume of the cylinder so formed is equal to \( (\text{Take } \pi = \frac{22}{7}) \)
(a) \( 2772 \text{ cm}^3 \)
(b) \( 2506 \text{ cm}^3 \)
(c) \( 2460 \text{ cm}^3 \)
(d) \( 2672 \text{ cm}^3 \)
Answer: (a)

Question. A toy is in the form of a cone mounted on a hemisphere of radius \( 7 \text{ cm} \). The total height of the toy is \( 14.5 \text{ cm} \). Find the volume of the toy. \( (\text{Take } \pi = \frac{22}{7}) \)
(a) \( \frac{539}{6} \text{ cm}^3 \)
(b) \( \frac{3311}{3} \text{ cm}^3 \)
(c) \( \frac{847}{6} \text{ cm}^3 \)
(d) \( 200 \text{ cm}^3 \)
Answer: (b)

Question. A cube whose edge is \( 20 \text{ cm} \) long, has circles on each of its faces painted black. What is the total area of the unpainted surface of the cube, if the circles are of the largest possible areas?
(a) \( 90.72 \text{ cm}^2 \)
(b) \( 256.72 \text{ cm}^2 \)
(c) \( 330.3 \text{ cm}^2 \)
(d) \( 514.28 \text{ cm}^2 \)
Answer: (d)

Question. In a swimming pool, base measuring \( 90 \text{ m} \times 40 \text{ m} \), \( 150 \) men take a dip. If the average displacement of water by a man is \( 8 \text{ m}^3 \), then rise in water level is
(a) \( 27.33 \text{ cm} \)
(b) \( 30 \text{ cm} \)
(c) \( 31.33 \text{ cm} \)
(d) \( 33.33 \text{ cm} \)
Answer: (d)

Question. The areas of three adjacent faces of a rectangular block are in the ratio of \( 2 : 3 : 4 \) and its volume is \( 9000 \text{ cu. cm} \), then the length of the shortest side is
(a) \( 10 \text{ cm} \)
(b) \( 12 \text{ cm} \)
(c) \( 15 \text{ cm} \)
(d) \( 18 \text{ cm} \)
Answer: (c)

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: (d)

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: (c)

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: (b)

Question. Eight solid spheres of the same size are made by melting a solid metalic 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)