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The Class 9 MCQ Questions of Surface Areas and Volumes with Answer will teach students about the connection between the length and expansiveness concerning various shapes and the incorporation of stature any place it is required.

Practice MCQ Questions for Class 9 Maths

1. In a cylinder, radius is doubled and height is halved, curved surface area will be

(a) halved
(b) doubled
(c) same
(d) four time

2. During conversion of a solid from one shape to another, the volume of the new shape will

(A) increase
(B) decrease
(C) remain unaltered
(D) be doubled

3. The radii of two cylinders are in the ratio of 2:3 and their heights are in the ratio of 5:3. The ratio of their volumes is:

(a) 10: 17
(b) 20: 27
(c) 17: 27
(d) 20: 37

4.  The total surface area of a cone whose radius is r/2 and slant height 2l is

(a) 2πr(l+r)
(b) πr(l+(r/4))
(c) πr(l+r)
(d) 2πrl

5. The lateral surface area of a cube is 256 m². The volume of the cube is

(a) 512 m³
(b) 64 m³
(c) 216 m³
(d) 256 m³

6. A cuboid having surface areas of 3 adjacent faces as a, b and c has the volume:

(a) 3\(\sqrt{abc}\)
(b) \(\sqrt{abc}\)
(c) abc
(d) (abc)²

7. The number of planks of dimensions (4 m × 50 cm × 20 cm) that can be stored in a pit that is 16 m long, 12m wide and 4 m deep is

(a) 1900
(b) 1920
(c) 1800
(d) 1840

8. A cone is 8.4 cm high and the radius of its base is 2.1 cm. It is melted and recast into a sphere. The radius of the sphere is

(a) 4.2 cm
(b) 2.1 cm
(c) 2. 4 cm
(d) 1.6 cm

9. The length of the longest pole that can be put in a room of dimensions (10 m × 10 m × 5m) is

(a) 15m
(b) 16m
(c) 10m
(d) 12m

10. The total surface area of a cube is 96 cm². The volume of the cube is:

(a) 8 cm³ 
(b) 512 cm³
(c) 64 cm³
(d) 27 cm³

11. Volume of spherical shell is

(a) 2/3 πr³
(b) 3/4 πr³
(c) 4/3 π(R³ – r³)
(d) None of these

12. Volume of hollow cylinder

(a) π(R² – r²)h
(b) πR²h
(c) πr²h
(d) πr²(h₁ – h₁)

13. The radius of a sphere is 2r, then its volume will be

(a) 4/3 πr³
(b) 4πr³
(c) 8/3 πr³
(d) 32/3 πr³

14. The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratio of the surface areas of the balloon in the two cases is

(a) 1:4
(b) 1:3
(c) 2:3
(d) 2:1

15. The surface area of a sphere of radius 14 cm is:

(a) 1386 sq.cm
(b) 1400 sq.cm
(c) 2464 sq.cm
(d) 2000 sq.cm

16. If slant height of the cone is 21cm and the diameter of the base is 24 cm. The total surface area of a cone is:

(a) 1200.77 sq.cm
(b) 1177 sq.cm
(c) 1222.77 sq.cm
(d) 1244.57 sq.cm

17. The diameter of the base of a cone is 10.5 cm, and its slant height is 10 cm. The curved surface area is:

(a) 150 sq.cm
(b) 165 sq.cm
(c) 177 sq.cm
(d) 180 sq.cm

18. The Curved surface area of a right circular cylinder is 4.4 sq.cm. The radius of the base is 0.7 cm. The height of the cylinder will be:

(a) 2 cm
(b) 3 cm
(c) 1 cm
(d) 1.5 cm

19. The curved surface area of a right circular cylinder of height 14 cm is 88 cm². The diameter of the base is:

(a) 2 cm
(b) 3cm
(c) 4cm
(d) 6cm

20. The radius of a hemispherical balloon increases from 6 cm to 12 cm as air is being pumped into it. The ratios of the surface areas of the balloon in the two cases is

(a) 1 : 4
(b) 1 : 3
(c) 2 : 3
(d) 2 : 1

Answer: 

1. Answer: (c) same

2. Answer:  (C) remain unaltered

Explanation: During conversion of one solid shape to another, the volume of the new shape will remain unaltered.

3. Answer: (b) 20: 27

Explanation: Given that, the radii of two cylinders are in the ratio of 2:3

Hence, r₁= 2r, r₂ = 3r

Also, given that, the height of two cylinders are in the ratio 5:3.

Hence, h₁ = 5h, h₂ = 3h

The ratio of the volume of two cylinders = V₁/V₂

= πr₁²h₁/πr₂²h₂

= [(2r)²(5h)]/[(3r)²(3h)]

Ratio of their volumes =(20r²h)/(27r²h) = 20/27 = 20: 27.

4. Answer: (b) πr(l+(r/4))

Explanation: The total surface area of cone = πr(l+r) square units.

If r = r/2 and l= 2l, then the TSA of cone becomes,

TSA of cone = π(r/2)[(2l+(2/r)]

=π[(rl)+(r2/4)]

TSA of new cone =πr[l+(r/4)]

5. Answer: (a) 512 m³

Explanation: The lateral surface area of cube = 4a²

4a²= 256

a² = 256/4 =64

a = 8 m

Hence, the volume of cube = a³ cube units 

V = 8³  = 512 m³.

6.  Answer:  (b) \(\sqrt{abc}\)

7. Answer: (b) 1920

Explanation: Volume of Plank = 400 cm×50cm×20cm=400000cm³

Volume of pits = 1600cm×1200cm×400cm = 768000000cm³

Number of planks = Volume of planks/Volume of pits

= 768000000/400000

Hence, the number of pits = 1920

8. Answer: (b) 2.1 cm

Explanation: Given that the height of cone = 8.4 cm

Radius of cone = 2.1 cm

Also, given that the volume of cone = volume of a sphere

(1/3)πr²h = (4/3)πr³

(1/3)π(2.1)2(8.4) = (4/3)πr³

37.044= 4r³

r³= 37.044/4

r³= 9.261

r = 2.1

Therefore, the radius of the sphere is 2.1 cm.

9. Answer: (a) 15m

Explanation: Given: l=10m, b= 10m, h= 5m

The length of the longest pole = √[10²+10²+5²]

= √(100+100+25) = √225 = 15 m.

10. Answer: (c) 64 cm³

Explanation: We know that the TSA of the cone = 6a².

6a² = 96 cm²

a² = 96/6 = 16

a =4 cm

The volume of cone = a³ cubic units

V = 4³ = 64cm³.

11. Answer: (c) 4/3 π(R³ – r³)

12. Answer: (a) π(R² – r²)h

13. Answer: (d) 32/3 πr³ 

14. Answer: (a) 1:4

Explanation: We know that the total surface area of the hemisphere = 3πr² square units.

If r= 6cm, then TSA = 3π(6)² = 108π

If r = 12 cm, then TSA = 3π(12)²= 432π

Then the ratio = (108π)/(432π)

Ratio = 1/4, which is equal to 1:4.

15. Answer: (c) 2464 sq.cm

Explanation: Radius of sphere, r = 14 cm

Surface area = 4πr²

= 4 x 22/7 x (14)² = 2464 sq.cm.

16. Answer: (d) 1244.57 sq.cm

Explanation: Total surface area = πr(l + r)

r = 24/2 = 12 cm

l = 21 cm

TSA = π(12)(21 + 12) = 1244.57 sq.cm

17. Answer: (b) 165 sq.cm

Explanation: Diameter = 10.5, Radius = 10.5/2

Slant height, l = 10cm

Curved surface area of cone = πrl = π(5.25)(10)

CSA = 165 sq.cm

18. Answer: (c) 1 cm

Explanation: Curved surface area of cylinder = 2πrh

2πrh = 4.4

h = 4.4/(2π x 0.7)

h = 1 cm

19. Answer: (a) 2 cm

Explanation: Curved surface area of cylinder = 88 sq.cm

Height = 14 cm

2πrh = 88

r = 88/2πh

r=1 cm

Diameter = 2r = 2cm

20. Answer: (a) 1 : 4

Click here to practice: – Surface Areas and Volumes MCQ Question for Class 9 Maths