Question

The slant height of a frustum of a cone is 3 cm and the perimeters of its circular ends are 20 cm and 16 cm. Find the curved surface area of the frustum.
1. 32 cm²
2. 54 cm²
3. 42 cm²
4. 33 cm²

Answer 1

Correct Answer - Option 2 : 54 cm²

Given:

Perimeter of upper circular end of frustum = 20 cm

Perimeter of lower circular end of frustum = 16 cm

Slant height (l) of frustum = 3 cm

Formula used:

Curved surface area of frustum = π(r₁ + r₂)l

Where, r₁ = Radius of upper base of frustum

r₂ = Radius of lower base of frustum

Perimeter of circle = 2

πr

Calculation:

Perimeter of upper circular end of frustum = 20 cm

⇒ 2πr₁ = 20

⇒ r1 = 10/π 

Again,

Perimeter of lower circular end of frustum = 16 cm

⇒ 2πr₂ = 16

⇒ r₂ = 8/π 

According to the question:

Curved surface area of frustum = π(r1 + r2)l

⇒ 3π (10/π + 8/π)

⇒ 3 × (18/π) × π 

⇒ 3 × 18 = 54

∴ The curved surface area of the frustum is 54 cm².