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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.

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Solution

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=18πR=9 ...(i)2πr=6πr=3 ....(ii)

Curved surface area of the frustum=πlR+r
=l×πR+πr=4×9+3 Since l=4 cm (from (i) and (ii))=48 cm2

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