CBSE Class 10 Mathematics Surface Areas and Volumes MCQs Set C

Question. The volume of a cube is numerically equal to its surface area. What is the length of its side?
(a) 6 units
(b) 8 units
(c) 9 units
(d) 10 units

Answer: A

Question. A solid sphere and a solid hemisphere have the same total surface area. Find the ratio of their volumes.
(a) √3 :1
(b) 3√3 :5
(c) 3√3 : 4
(d) 1: √3

Answer: C

Question. A cone and a hemisphere have equal bases and equal volumes. Identify the ratio of their heights.
(a) 1 : 3
(b) 1 : 2
(c) 2 : 1
(d) 3 : 1

Answer: C

Question. The diameter of a copper sphere is 6 cm. It is beaten and drawn into a wire of diameter 0.2 cm. What is the length of the wire?
(a) 36cm
(b) 360cm
(c) 3600 cm
(d) 306 cm

Answer: C

Question. A hemispherical bowl is made of steel of 0.25 cm thickness. The inner radius of the bowl is 5 cm. What is the volume of steel used?
(a) 42.15 cm³
(b) 41.52 cm³
(c) 41.25cm³
(d) 43.21cm³

Answer: C

Question. If the radii of the circular ends of a conical bucket of height 45 cm are 28 cm and 7 cm, what is the capacity of the bucket?
(a) 48150cm³
(b) 48510cm³
(c) 48105cm³
(d) 48015cm³

Answer: B

Question. A cylindrical vessel contains 49.896 litres of liquid. The cost of painting its curved surface area at 2 paise/sq cm is ` 95.04. Find its total surface area.
(a) 5724 cm²
(b) 7524 cm²
(c) 5742 cm²
(d) 7254 cm²

Answer: B

Question. A piece of metal pipe is 77 cm long with inside diameter of the cross section as 4 cm. If the outer diameter is 4.5 cm and the metal weighs 8 gm/cu cm, find the weight of pipe.
(a) 2.057 kg
(b) 20.57 kg
(c) 205.7 kg
(d) 2.097 kg

Answer: A

Question. Two right circular cones X and Y are made such that X has a radius three times the radius of Y and Y has a volume half the volume of X. What is the ratio of heights of X and Y?
(a) 5 : 8
(b) 4 : 7
(c) 2 : 9
(d) 3 : 5

Answer: C

Question. If the radius of the base of a right circular cylinder is halved, keeping the height same, find the ratio of the volume of the reduced cylinder to that of the original cylinder.
(a) 1 : 4
(b) 2 : 3
(c) 1 : 2
(d) 5 : 7

Answer: A

Question. A sphere, of diameter 12 cm, is dropped into a right circular cylindrical vessel, partly filled with water. If the sphere is completely immersed in water, the water level in the cylindrical vessel rises by 3(5/9) cm. Find the diameter of the cylindrical vessel.
(a) 16cm
(b) 18cm
(c) 12cm
(d) 13cm

Answer: B

Question. The largest possible cube is made from a wooden sphere of radius 6√3cm cm. Find the surface area of the cube.
(a) 864cm²
(b) 542cm²
(c) 735cm²
(d) 625cm²

Answer: A

Question. The internal and external radii of a hemispherical metallic vessel are 7 cm and 10.5 cm respectively. If 3 1 cm of the metal weighs 10 g, find the weight of the vessel.
(a) 25.15 kg
(b) 32.1 kg
(c) 17.07 kg
(d) 16.27 kg

Answer: C

One Word Questions :

Question. Curved surface area of cylinder is 16 cm². Its radius is 4cm, then find its height.
Answer: 2cm

Question. The Circumference of the circular edge of solid hemispherical ball is 132cm. Find the radius of ball.
Answer: 21cm

Question. Find the slant height of a cone, if height 12cm and radius is 5cm.
Answer: 13cm

Question. What will be the area of four walls of a room of length 12m, breadth 10m and height 9m?
Answer: 396m²

Question. Three cubes of the same metal, whose edges are 6, 8, 10cm are melted and formed into a single cube. Find the diagonal of the single cube.
Answer: 12 √3cm

Question. 500 persons took dip in a rectangular tank which is 80m long and 50m broad. What is the rise in level of water in the tank if the average displacement of water by a person is 0.04m³ ?
Answer: 0.5cm or .005m

Question. If the radius and height of a cylinder are in the ratio 2 : 7 and its volume is 88m³ , then what will be its radius?
Answer: 2m

Question. 50 circular plates each of equal radius are placed one over the other to form a cylinder. Find the height of the cylinder so formed, thickness of each plate is 1/2cm.
Answer: 25cm

Question. Find the volume of cone of height 2h and radius r.
Answer: 2/3 r2h

Question. If a sphere of diameter 12cm is melted and drawn into a wire of diameter 0.2cm, find the length of the wire.
Answer: 288m

Question. The volume of cube is 8a3 , find its edge.
Answer: 2a

Question. The volume of a room is 5760m³ . Its length and width are 24m and 20m, find the height.
Answer: 12m

Question. A right cylindrical vessel is full of water. How many right cones having the same diameter and height as those of the right cylinder will be needed to store that water?
Answer: 3