Surface Area of Cone

Solved Questions of Surface Area of Cone

1. If Robert makes a cone with a radius of 5 cm and a slant height of 8 cm. What is the curved surface area of this cone?

a) 10π cm²
b) 20π cm²
c) 30π cm²
d) 40π cm²

Answer: d)  40π cm²

Explanation: Curved surface area = πrL
Substituting the given values, we get:
Curved Surface Area = π(5)(8) = 40π cm²

Therefore, the curved surface area of the cone is 40π cm².

2. What is the total surface area of a cone with a radius of 8 cm and a slant height of 14 cm?

a) 320π cm²
b) 604π cm²
c) 210π cm²
d) 176π cm²

Answer: d) 176π cm²

Explanation: Total surface area of a cone = πr(r + L)
= π x 8(8 + 14)
= 176 π cm²

3. A cone has a radius of 5 cm and a slant height of 12 cm. What is the curved surface area of the cone?

a) 188.5 cm²
b) 204 .23 cm²
c) 210.8 cm²
d) 376. 2 cm²

Answer: a) 188.5 cm²

Explanation: Using the formula, we get:
Curved Surface Area = πrL
= π (5 cm) (12 cm)
= 60π cm² = approximately 188.5 cm².

4. A circular cone is having 15 inches slant height and the radius of the base is 20 inches. What is the lateral surface area of the cone?

a) 942 inch²
b) 924 inch²
c) 723 inch²
d) 787 inch²

Answer: a) 942 inch² 

Explanation: The lateral surface area of cone is given by:
LSA = π × r × l
LSA =3.14 × 20 × 15
LSA = 942 inch²

5. A cone has a radius of 3 cm and a height of 5 cm, find the total surface area of the cone.

a) 58.3 cm²
b) 78.3 cm²
c) 83.17 cm²
d) 98.32 cm²

Answer: c) 83. 17 cm²

Explanation: We need to find the slant height of the cone,
We need to use Pythagoras’ theorem to calculate it, since the cross-section is a right triangle.

l² = h² + r²
l² = 5² + 3²
l² = 25 + 9
l = √(34)
l = 5.83 cm

And the total surface area of the cone is:
TSA = πr² + πrl
TSA = π · r · (r + l)
TSA = π · 3 · (3 + 5.83)
TSA = 83.17 cm

Practice Questions of Surface Area of Cone

1. A cone of radius 3 cm and slant height 5 cm. What is curved surface area?

a) 13π cm²
b) 15π cm²
c) 17π cm²
d) 21π cm²

Answer: b) 15π cm²  

2. The slant height of a cone is 20 cm. The diameter of the base is 15 cm. Find the curved surface area of the cone.

a) 271 cm²
b) 391 cm²
c) 471 cm²
d) 561 cm²

Answer: c)  471 cm²

3. What is the total surface area of a cone with radius 4 cm and slant height 8 cm?

a) 142.32 cm²
b) 147.72 cm²
c) 150.12 cm²
d) 150.72 cm²

Answer: d) 150.72 cm²

4. What is the height of a cone if its radius is 14 units, and its curved surface area is 1100 square units?

a) 20.71 units
b) 18.23 units
c) 15.23 units
d) 10.31 units

Answer: a) 20.71 units

5. Find the area of the curved surface of a cone with a radius of 8.5 cm and a slant height of 22 cm.

a) 507.06 cm²
b) 557.16 cm²
c) 587.71 cm²
d) 607.26 cm²

Answer: c) 587.71 cm²

6. Find the lateral surface area of the given figure in cm².

a) 10π
b) 20π
c) 30π
d) 40π

Answer: b) 20π

7. Find the total surface area of a right cone if the radius is 6 inches and the slant height is 10 inches.

a) 96π in²
b) 106π in²
c) 108π in²
d) 169π in²

Answer: a) 96π in²

8. Find the total surface area of a cone with a radius of 4 inches and a slant height of 6 inches.

a) 125.7 in²
b) 152.8 in²
c) 165.2 in²
d) 178.2 in²

Answer: a) 125.7 in²

9. Find the total surface area of a cone with a radius of 3 inches and a slant height of 4.5 inches.

a) 51.7 in²
b) 70.7 in²
c) 79.3 in²
d) 82.1 in²

Answer: b) 70.7 in²

10. A cone has a radius of 8 cm and a height of 15 cm. What is its surface area?

a) 288π cm²
b) 320π cm²
c) 200π cm²
d) 384π cm²

Answer: c) 200π cm²