CBSE Class 9 Maths Surface Areas and Volumes MCQs Set D

Question. A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water will fall into the sea in a minute?
(a) 4000 m³
(b) 40 m³
(c) 400 m³
(d) 40000 m³

Question. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold?
(a) 33.75 litre
(b) 34.65 litre
(c) 35.75 litre
(d) 38.75 litre

Question. If the lateral surface of a cylinder is 94.2 cm² and its height is 5 cm, then find radius of its base
(a) 5cm
(b) 4cm
(c) 3cm
(d) 6cm

Question. It costs Rs 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of Rs 20 per m2, find radius of the base,
(a) 1.75 m
(b) 1.85 m
(c) 1.95 m
(d) 1.65 m

Question. The height and the slant height of a cone are 21 cm and 28 cm respectively. Find the volume of the cone.
(a) 5546 cm³
(b) 7546 cm³
(c) 5564 m³
(d) 8546 cm³

Question. Find the volume of the right circular cone with radius 6 cm, height 7 cm
(a) 254 cm³
(b) 264 cm³
(c) 274 cm²
(d) 284 cm³

Question. The radius and height of a conical vessel are 7 cm and 25 cm respectively. Its capacity in litres is
(a) 1.232 litre
(b) 1.5 litre
(c) 1.35 litre
(d) 1.6 litre

Question. The height of a cone is 15 cm. If its volume is 1570 cm³, find the radius of the base.
(a) 12 cm
(b) 10 cm
(c) 15 cm
(d) 18 cm

Question. If the volume of a right circular cone of height 9 cm is 48π cm³, find the diameter of its base.
(a) 12 cm
(b) 10 cm
(c) 6 cm
(d) 8 cm

Question. A conical pit of top diameter 3.5 m is 12 m deep. What is its capacity in kilolitres?
(a) 38.5 kl
(b) 48.5 kl
(c) 39.5 kl
(d) 47.5 kl

Question. Find the capacity in litres of a conical vessel with radius 7 cm, slant height 25 cm
(a) 1.232 litre
(b) 1.5 litre
(c) 1.35 litre
(d) none of these

Question. The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?
(a) 1/64 
(b) 1/ 32   
(c) 1/16 
(d) 1/48

Question. The dimensions of a cuboid are 50 cm x 40 cm x 10 cm. Its volume in litres is:
(a) 10 litres
(b) 12 litres
(c) 20 litres
(d) 25 litres

Question. The volume of a cuboidal tank is 250 m³. If its base area is 50 m² then depth of the tank is
(a) 5 m
(b) 200 m
(c) 300 m
(d) 12500 m

Question. The length, breadth and height of a cuboidal solid is 4 cm, 3 cm and 2 cm respectively. Its volume is
(a) (4 + 3 +2) cm³
(b) 2(4 + 3 +2) cm³
(c) (4 x 3 x 2) cm³
(d) 2(4 + 3) x 2 cm³

Question. The volume of a cuboidal solid of length 8 m and breadth 5 m is 200 m³. Find its height.
(a) 5 m
(b) 6 m
(c) 15 m
(d) 18 m

Question. The curved surface area of a sphere is 616 cm². Its radius is
(a) 7 cm
(b) 5 cm
(c) 6 cm
(d) 8 cm

Question. If radius of a sphere is 2d/3 then its volume is
(a) 32/81πd³
(b) 23/4πd³
(c) 32/3πd³
(d) 34/3πd³

Question. The capacity of a cylindrical tank is 6160 cm³. Its base diameter is 28 m. The depth of this tank is
(a) 5 m
(b) 10 m
(c) 15 m
(d) 8 m

Question. The volume of a cylinder of radius r and length h is:
(a) 2πrh
(b) 4/3πr²h
(c) πr²h
(d) 2πr²h

Question. Base radius of two cylinder are in the ratio 2 : 3 and their heights are in the ratio 5 : 3. The ratio of their volumes is
(a) 27 : 20
(b) 25 : 24
(c) 20 : 27
(d) 15 : 20

Question. If base radius and height of a cylinder are increased by 100% then its volume increased by:
(a) 30%
(b) 40%
(c) 42%
(d) 33.1%

Question. The diameter of a sphere is 14 m. The volume of this sphere is 
(a) 1437 1/3 m³
(b) 1357 1/3 m³
(c) 1437 2/3 m³
(d) 1337 2/3 m³

Question. The volume of a sphere is 524 cm3. The diameter of sphere is
(a) 5cm
(b) 4cm
(c) 3cm
(d) 7cm

Question. The total surface area of a cylinder is 40π cm². If height is 5.5 cm then its base radius is
(a) 5cm
(b) 2.5cm
(c) 1.5cm
(d) 10cm

Question. The area of circular base of a right circular cone is 78.5 cm². If its height is 12 cm then its volume is
(a) 31.4 cm³
(b) 3.14 cm³
(c) 314 cm³
(d) none of these

Question. The base radius of a cone is 11.3 cm and curved surface area is 355 cm². Its height is (Take π = 355/113)
(a) 5 cm
(b) 10 cm
(c) 11 cm
(d) 9 cm

1. The space occupied by a solid body is called its volume. The units of volume are cubic centimetre (cm³) or cubic metres (m³) etc.

2. Cuboid : A solid bounded by six rectangular plane faces is called a cuboid.

3. Cube : A cuboid whose length, breadth and height are all equal is called a cube.

4. Cuboid : For a cuboid of length = l units, breadth = b units and height = h units.
(i) Volume of cuboid = (l × b × h) cubic units
(ii) Diagonal of the cuboid = √l² + b² + h² units
(iii) Total surface area of the cuboid = 2(lb + bh + lh) sq units
(iv) Lateral surface area of the cuboid = [2(l + b) × h] sq units
(v) Area of 4 walls of a room = [2(l + b) × h] sq units

5. Cube : For a cube of edge = a units
(i) Volume of the cube = a3 cubic units
(ii) Diagonal of the cube = a √3 units
(iii) Total surface area of the cube = (6a²) sq units
(iv) Lateral surface are of the cube = (4a²) sq units
Relation between units
Length units Volume units
1 cm = 10 mm 1 cm² = 1000 mm³
100 cm = 1 m 1 m³ = 1000000 cm³
1 litre = 1000 cm³
1 kilolitre = 1000 litres = 1 m³

6. Cylinder : A solid having a curved surface as a lateral surface and a uniform circular cross-section is known as a cylinder

b If the axis of the cylinder is perpendicular to each cross-section then the cylinder is called a right circular cylinder

7. Volume of a cylinder : For a cylinder whose height is a h units and the radius of whose base is r units, Volume of cylinder = (πr²h) cubic units = (base area) × height

8. Surface area of cylinder : For a cylinder of height h and radius r :
(a) Area of curved surface = (2 πrh) sq units
(b) Total surface area = (2πrh + 2π r²) sq units

9. Cone : It is a solid having a plane circular end as the base and whose lateral surface is a curved surface tapering into a point, called its vertex. 

Note : For a right circular cone, we have AO is perpendicular to OB, i.e., ΔAOB is right angled at O. Hence, l² = r² + h²

10. Volume of a cone : For a cone of radius r units and height h units, volume of cone = (1/3 πr²h) cubic units.

11. Area of curved surface : For a cone of radius r, height h and slant height l,
(a) Area of curved surface = prl sq units
(b) Total surface area = (πrl + πr2) sq units

12. (a) Sphere : The set of all points in space equidistant from a fixed point is called a sphere.
(b) Hemisphere : A plane through the centre of a sphere cuts it into two equal parts. Each part is called a hemisphere.
(c) Spherical shell : The difference of two solid concentric spheres is called a spherical shell. 

13. For a sphere of radius r units : 
(a) Volume of sphere = (1/3πr³) cubic units
(b) Area of curved surface of the sphere = (4πr²) cubic units
(c) Volume of the hemisphere = (1/3πr3)cubic units
(d) Curved surface of the hemisphere = (2πr²) sq units
(e) Total surface area of the hemisphere = 2πr² + πr² = (3πr²) sq units

Question. A cooking pot has a spherical bottom, while the upper part is a truncated cone. Its vertical crosssection is shown in the figure. If the volume of food increases by 15% during cooking, the maximum initial volume of food that can be cooked without spilling is (in cc) 

(A) 14450 π/3
(B) 19550  π/3
(C) 340000/69π
(D) 20000/3 π

Answer: D

Question. Each side of a cube is increased by 50%. Then the surface area of the cube increases by
(A) 50%
(B) 100%
(C) 125%
(D) 150%

Answer: C

Question. Three cylinders each of height 16 cm and radius of base 4 cm are placed on a plane so that each cylinder touches the other two. Then the volume of region enclosed between the three cylinders in cm³ is
(A) 98(4 √3 - π)
(B) 98(2 √3 - π)
(C) 98( √3 - π)
(D) 128(2 √3 - π)

Answer: D

Question. Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved a distance equal to half the longer side. Then the ratio of the shorter side to the longer side is
(A) 1/2
(B) 2/3
(C) 1/4
(D) 3/4

Answer: D

Question. The number of surfaces in right circular cylinder is 
(A) 1
(B) 2
(C) 3
(D) 4

Answer: C

Question. 

Fields X and Y are to be enclosed with a fencing at the cost of Rs 40 per meter. If the cost on field X is denoted by Cx and that on field Y is denoted by Cy we have 
(A) C_x = C_y
(B) C_x < C_y
(C) C_x > C_y
(D) cannot be determined 

Answer: A

Question. A covered wooden box has the inner measures as 115 cm, 75 cm and 35 cm. Find the volume of the wood.
(A) 80,000 cu cm
(B) 82,125 cu cm
(C) 84,000 cu cm
(D) 85,000 cu cm

Answer: B

Question. The edge of a cube is 20 cm. How many small cubes of 5 cm edge can be formed from this cube?
(A) 4
(B) 32
(C) 64
(D) 100

Answer: C

Question. Two cylinders of same volume have their heights in the ratio 1 : 3. Find the ratio of their radii.
(A) √3 :1
(B) √2 :1
(C) √5 : 2
(D) 2: √5

Answer: A

Question. A metallic right circular cone of height 9 cm and base radius 7 cm is melted into a cuboid whose two sides are 11 cm and 6 cm. What is the third side of the cuboid?
(A) 5 cm
(B) 6 cm
(C) 7 cm
(D) 10 cm

Answer: C

Question. The slant height of a cone is increased by P%. If radius remains same, the curved surface area is increased by
(A) P%
(B) P2%
(C) 2P%
(D) None

Answer: A

Question. The volumes of two spheres are in the ration 64 : 27. Find the difference of their surface areas, if the sum of their radii is 7 units
(A) 28π sq units
(B) 88 sq units
(C) 88π sq units
(D) 4π sq units

Answer: A

Question. In the figure below, LMNO and GHJK are rectangles where GH = 1/2 LM and HJ = 1/2 MN. What fraction of the region is bounded by LMNO that is not shaded?
(A) 1/4
(B) 1/3
(C) 1/2
(D) 3/4

Answer: D

Question. In the figure below, RSTV is a square inscribed in a circle with centre O and radius r. The total are of shaded region is
(A) r²(π – 2)
(B) 2r(2 – π)
(C) π(r² – 2)
(D) π r² – 8r 

Answer: A

Question. A right circular cone of diameter K cm and height 12 cm rests on the base of a right circular cylinder of radius K cm (their bases lie in the same plane, as shown in figure). The cylinder is filled with water to a height of 12 cm. If the cone is then removed, the height to which water will fall is 

(A) 11 cm
(B) 10 cm
(C) 8 cm
(D) cannot be determined from given data

Answer: A

Question. The ratio of radii of two cylinders is 1 : √3 and heights are in the ratio 2 : 3. The ratio of their volumes is
(A) 1 : 9
(B) 2 : 9
(C) 4 : 9
(D) 5 : 9

Answer: B

Question. The dimensions of a hall are 40 m, 25 m and 20 m. if each person requires 200 cubic metre, then the number of persons who can be accommodated in the hall are
(A) 120
(B) 150
(C) 140
(D) 100

Answer: D

Question. Correct the perimeter of the figure given below to one decimal place. 

(A) 56.0 m
(B) 56.6 m
(C) 57.2 m
(D) 57.9 m

Answer: B

Question. A hollow spherical ball whose inner radius is 4 cm is full of water. Half of the water is transferred to a conical cup and it completely filled the cup. If the height of the cup is 2 cm, then the radius of the base of cone, in cm is
(A) 4
(B) 8π
(C) 8
(D) 16

Answer: C

Question. The largest volume of cube that can be inclosed in a sphere of diameter 2 cm is (in cm³)
(A) 1
(B) 2 √2
(C) π
(D) 8/3√3

Answer: B

Question. The radius of the cylinder whose lateral surface area is 704 cm² and height 8 cm is
(A) 6 cm
(B) 4 cm
(C) 8 cm
(D) 14 cm

Answer: D

Question. The radius of a sphere is increased by P%. Its surface area increases by
(A) P%
(B) P2%
(C) 8(2P+P²/100)%
(D) P²/P %

Answer: C

Question. The radius of cylinder is doubled but its lateral surface area is unchanged. Then its height must be
(A) doubled
(B) halved
(C) tribled
(D) constant

Answer: B

Question. The height and radius of a cone are 3 cm and 4 cm respectively. Its curved surface area must be is
(A) 62x 6/7 sq cm
(B) 57x 3/4 sq cm
(C) 6 cm²
(D) 12 cm²

Answer: A