Question

The slant height of the frustum of a cone is 4 cm and the perimeters (i.e. circumferences) of its circular ends are 18 cm and 6 cm. Find the curved surface area of the frustum.

Answer 1

Let R and r be the radii of the top and base of the frustum of the cone, respectively, and its slant height be l.

Then,

2πR = 18 ⇒ πR = 9   .....(i)

2πR = 6 ⇒ πr = 3     .....(ii)

Curved surface area of the frustum =πl (R + r)

= l × (πR + πr )

= 4 × (9 + 3)   [Since l = 4 cm]  (From (i) and (ii))

= 48 cm²