CBSE Class 10 Mathematics Surface Area and Volume Assignment Set A

Questiom. The volume of a cube is 2744 cm³. Its surface area is
(a) 196 cm²
(b) 1176 cm²
(c) 784 cm²
(d) 588 cm²

Answer: B

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

Answer: D

Questiom. The height of a cylinder is 14 cm and its curved surface area is 264 cm². The volume of the cylinder is
(a) 296 cm³
(b) 396 cm³
(c) 369 cm³
(d) 503 cm³

Answer: B

Questiom. 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

Questiom. 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

Questiom. The base radius of the cylinder is 1(2/3) times its height. The cost of painting its C.S.A. at 2 paise/cm² is ₹ 92.40. The volume of the cylinder is
(a) 80850 cm³
(b) 88850 cm³
(c) 80508 cm³
(d) none of the options

Answer: A

Questiom. A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. The radius of the third ball is
(a) 1.5 cm
(b) 2 cm
(c) 3 cm
(d) 2.5 cm

Answer: D

Questiom. A circus tent is cylindrical up to a height of 4 m and conical above it. If its diameter is 105 m and its slant height is 40 m, the total area of canvas required to built the tent is
(a) 7920 m2
(b) 7820 m2
(c) 9720 m2
(d) 2645 m2

Answer: A

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

Answer: A

Questiom. The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is 5 cm, then height of the cone is
(a) 10 cm
(b) 15 cm
(c) 18 cm
(d) 24 cm

Answer: B

Questiom. A cylindrical vessel 16 cm high and 9 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 cm, the radius of its base is
(a) 12 cm
(b) 18 cm
(c) 36 cm
(d) 48 cm

Answer: B

Questiom. The volume of the greatest sphere that can be cut off from a cylindrical log of wood of base radius 1 cm and height 5 cm is
(a) 4/3  cm³
(b) 10/3  cm³
(c) 5π cm³
(d) 20/3  cm³

Answer: A

Questiom. 12 spheres of the same size are made from melting a solid cylinder of 16 cm diameter and 2 cm height. The diameter of each sphere is
(a) 3 cm
(b) 2 cm
(c) 3 cm
(d) 4 cm

Answer: D

Questiom. A rectangular sheet of paper 44 cm × 18 cm is rolled along its length and a cylinder is formed.
The volume of the cylinder so formed is equal to (Take π = 22/7)
(a) 2772 cm³
(b) 2506 cm³
(c) 2460 cm³
(d) 2672 cm³

Answer: A

Questiom. A toy is in the form of a cone mounted on a hemisphere of radius 7 cm. The total height of the toy is 14.5 cm. Find the volume of the toy. (Take π = 22/7)
(a) (539/6)cm³
(b) (3311/3)cm³
(c) (847/6)cm³
(d) 200 cm³

Answer: B

Questiom. A cube whose edge is 20 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 cm²
(b) 256.72 cm²
(c) 330.3 cm²
(d) 514.28 cm²

Answer: D

Questiom. In a swimming pool, base measuring 90 m × 40 m, 150 men take a dip. If the average displacement of water by a man is 8 m³, then rise in water level is
(a) 27.33 cm
(b) 30 cm
(c) 31.33 cm
(d) 33.33 cm

Answer: D

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

Answer: C

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

Answer: C

Questiom. The height of a conical tent is 14 m and its floor area is 346.5 m². The length of canvas, 1.1 m wide, required for it is
(a) 490 m
(b) 525 m
(c) 665 m
(d) 860 m

Answer: B

Questiom. A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 3.5 cm, height 3 cm. The number of cones so formed is
(a) 405
(b) 540
(c) 504
(d) none of the options

Answer: C

Questiom. A metal sheet 27 cm long, 8 cm broad and 1 cm thick is melted into a cube. The difference between surface areas of two solids is
(a) 284 cm²
(b) 285 cm²
(c) 286 cm²
(d) 287 cm²

Answer: C

Questiom. The curved surface area of a cylinder is 264 m² and its volume is 924 m³. The ratio of its diameter to its height is
(a) 3 : 7
(b) 7 : 3
(c) 6 : 7
(d) 7 : 6

Answer: B

Questiom. The radius of spherical balloon increases from 8 cm to 12 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

Questiom. If two cubes, each of edge 4 cm are joined end to end, then the surface area of the resulting cuboid is
(a) 100 cm²
(b) 160 cm²
(c) 200 cm²
(d) 80 cm²

Answer: B

Questiom. A cylindrical pillar of a temple is shown in the figure, which is conical at the top. Then the curved surface area of the pillar is
(a) 70 p m²
(b) 76 p m²
(c) 72 p m²
(d) 75 p m²

Answer: D

Questiom. A solid is in the form of a cylinder with hemispherical ends. The total height of the solid is 16 cm and the diameter of the cylinder is 7 cm. Then the total surface area of the solid is
(a) 324 cm²
(b) 464 cm²
(c) 418 cm²
(d) 352 cm²

Answer: D

Questiom. A vessel is in the form of a hollow hemisphere mounted by a hollow cylinder. The diameter of the hemisphere is 42 cm and the total height of the vessel is 30 cm. Find the inner surface area of the vessel.
(a) 3500 cm²
(b) 3800 cm²
(c) 3960 cm²
(d) 3900 cm²

Answer: C

Questiom. 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 : 3
(c) 1 : 1
(d) 3 : 1

Answer: B

Questiom. The volume of the largest right circular cone that can be cut out from a cube of edge 4.2 cm is
(a) 9.7 cm³
(b) 72.6 cm³
(c) 58.2 cm³
(d) 19.4 cm³

Answer: D

Questiom. The volume of the largest right circular cone that can be carved out of a solid hemisphere of radius r is
(a) (4/3)πr³
(b) (2/3)πr³
(c) 4πr²
(d) (1/3)πr³

Answer: B

Questiom. 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: B

Questiom. How many spherical lead shots each 4.2 cm in diameter can be obtained from a solid cuboid with dimensions 66 cm, 42 cm and 21 cm?
(a) 1500
(b) 750
(c) 500
(d) 2000

Questiom. The number of solid spheres, each of diameter 6 cm that could be moulded to form a solid metal cylinder of height 54 cm and diameter 4 cm, is
(a) 3
(b) 4
(c) 5
(d) 6

Questiom. Eight solid spheres of the same size are made by melting a solid metalic cylinder of base diameter 6 cm and height 32 cm. The diameter of each sphere is
(a) 3 cm
(b) 6 cm
(c) 12 cm
(d) 8 cm

Questiom. The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is 8 cm, then height of the cone is
(a) 10 cm
(b) 15 cm
(c) 18 cm
(d) 24 cm

Questiom. A hollow cylinder of height 15 cm is melted and cast into a solid cylinder of height 3 cm. If the internal and external radii of the hollow cylinder are 2 cm and 3 cm respectively, then the radius of the solid cylinder is
(a) 1 cm
(b) 5 cm
(c) 3 cm
(d) 4 cm

LEVEL (1)

1. Two cubes each with 12cm. edge are joined end to end. Find the surface area of the resulting cuboid.
2. Three cubes of metal whose edges are 3cm., 4cm. and 5cm. are melted and formed into a single cube. Find its edge.
3. Find the curved surface area of a right circular cylinder of height 13.5 cm. and radius of whose base is 7 cm.
4.The radii of end of frustum of a cone 40 cm high are 20 cm and 11 cm. Find its slant height.

SOLUTIONS

1. Length of resulting cuboid = 12+12 =24cm.
Breadth= 12cm. Height = 12cm
S.A. of resulting cuboid = 2(lb+bh+hl)
=2(288+144+288)
=2 x 720
=1440 cm.²

2. Volume of new cube= Volume of 3 cubes
= 3³+ 4³ +5³
=27+64+125
=216 cm.3
Side of new cube = 3√216
= 6 cm.

3. height of cylinder (h)=13.5 cm.

Radius of base (r) = 7 cm.
C.S.A of cylinder = 2πrh
=2 x 22/7 x 7 13.5
= 704 cm.

4. The radii of end of frustum of a cone 40 cm high are 20 cm and 11 cm. Find its slant height.

Please click the link below to download CBSE Class 10 Mathematics Surface Area and Volume Assignment Set A