Correct Answer - Option 2 : 54 cm
2
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.