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.
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.
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