Question

The slant height of the frustum of a cone is 4 cm and the perimeters of its circular ends are 18 cm and 6 cm. Find the curved surface of the frustum. 

Answer 1

Given,

Slant height of frustum of cone (l) = 4 cm

Let ratio of the top and bottom circles be r₁ and r₂

And given perimeters of its circular ends as 18 cm and 6 cm

⟹ 2πr₁ = 18 cm; 2πr₂ = 6 cm

⟹ πr₁= 9 cm and πr₂ = 3 cm

We know that,

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

= π(r₁ + r₂)l

= (πr₁+πr₂)l = (9 + 3) × 4 = (12) × 4 = 48 cm²

Therefore, the curved surface area of the frustum = 48 cm².