Volume of Cone

Solved Questions of Volume of a Cone

1. Find the volume of the cone shown below.

a) 1023.2 cm³
b) 1206.8 cm³
c) 1345 cm³
d) 1897.2 cm³

Answer: b) 1206.8 cm³

Explanation: From the figure, we know that,
Radius (r) = 8 cm
Height, (h) = 18 cm

We know the volume of a cone, (V) = (1/3) πr²h
V = (1/3) x (22/7) x (8²) x (18)
= (1/3) x (22/7) x (64) x (18)
= 1206.8 cm³

2. Find the volume of the cone. If the height and the slant height of a cone are 18 cm and 21 cm respectively.

a) 2203.57 cm³
b) 2230.57 cm³
c) 2032.57 cm³
d) 2003.57 cm³

Answer: a) 2203.57 cm³ 

Explanation: We know that
l ² = r² + h²
r² =√(l² - h²)
r = √(21² - 18²)
r = √(441 – 324)
r = √117
r = 10.81 cm

Volume of a cone is = (1/3) πr²h = (1/3) x (22/7) x (10.81)² x 18
= 2203.57 cm³

3. The height of a cone is 21 cm. If its volume is 2662 cm³, find the radius of the base (r).

a) 6.26 cm
b) 8 cm
c) 11 cm
d) 7 cm

Answer: c) 11 cm

Explanation: Height of the cone (h) = 21 cm
We know that the volume of a cone is:
V = (1/3) πr²h
π = 22/7
2662 = (1/3) x (22/7) x r² x 21
r² = (2662 x 3 x 7) / (21 x 22)
r² = 121
r = 11 cm

4. If the volume of a cone is 1232 cm³ and the radius of the base is 7 cm. Find the slant height of the cone.

a) 28 cm
b) 25 cm
c) 34 cm
d) 36 cm

Answer: b) 25 cm

Explanation: The radius of the base is = 7 cm
We know that the volume of a cone is
V = (1/3) πr²h
1232 = (1/3) x (22/7) x 7² x h
h = (1232 x 7 x 3) / (22 x 49)
h = 24 cm

We know that,
l ² = r² + h²
l = √(7² + 24²)
l = √(49 + 576)
l = √(625)
l = 25 cm

5. Find the volume of a cone where r = 6 cm and h = 7 cm. (Take π = 3.14)

a) 223.6 cm³
b) 129.03 cm³
c) 259.86 cm³
d) 263.76 cm³

Answer: d) 263.76 cm³

Explanation: By using the formula for the volume of a cone, we get:
V = (1/3) πr² h
Here, r = 6 cm, h = 7 cm
V= 1/3 x 3.14 x 6 x 6 x 7
= 1/3 x 791.28 = 263.76 cm³

Practice Questions of Volume of a Cone

1. If the volume of a cone is 48π cm³ and the height is 100 cm. Find the radius of its base.

a) 1.2 cm
b) 3.79 cm
c) 4.85 cm
d) 5.6 cm

Answer: a) 1.2 cm

2. If the radius is 3.5 cm and the height is 12 cm. Find the volume of the cone.

a) 114 cm³
b) 124 cm³
c) 137 cm³
d) 154 cm³

Answer: d) 154 cm³

3. The circumference of the base of a 44 cm high wooden solid cone is 94.2 cm. Find the volume.

a) 4500π cm³
b) 3300π cm³
c) 4137π cm³
d) 3800π cm³

Answer: b) 3300π cm³

4. A cone has a diameter of 8 cm and a height of 12 cm. What is its volume?

a) 64π cm³
b) 128π cm³
c) 256π cm³
d) 512π cm³

Answer: a) 64π cm³

5. A cone has a slant height of 10 cm and a height of 8 cm. What is its volume?

a) 96π cm³
b) 240π cm³
c) 120π cm³
d) 320π cm³

Answer: a) 96π cm³

6. A cone has a volume of 150π cm³ and a height of 9 cm. What is its radius?

a) 3√2 cm
b) 5√2 cm
c) 9√2 cm
d) 12√2 cm

Answer: b) 5√2 cm

7. Harry is filling a conical bag with gems. He knows the capacity of each bag is 54π in³. Help him in finding the height of the conical bag if its radius is 3 inches.

a) 14 cm
b) 13 cm
c) 18 cm
d) 11 cm

Answer: c) 18 cm

8. The radius and the height of a right circular cone are in the ratio 5:12. If its volume is 314 m³, find the slant height and the radius. (Use π = 3.14).

a) 13 m, 5 m
b) 12 m, 5 m
c) 6 m, 8 m
d) 12 m, 13 m

Answer: a) 13 m, 5 m

9. The radius and slant height of a cone is 10 ft and 26 ft long, respectively. What is the volume of the cone in terms of π?

a) 1200π ft³
b) 400π ft³
c) 600π ft³
d) 800π ft³

Answer: d) 800π ft³

10. What is the approximate volume of the cone with a diameter that is 50 ft long and a height of 12 ft? (Use π = 3.14).

a) 54800 ft³
b) 49800 ft³
c) 28800 ft³
d) 7850 ft³

Answer: d) 7850 ft³