Question

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

Answer 1

Slant height of frustum(l) = 4 cm

Perimeter of upper top = 18 cm

$\Rightarrow 2\pi R=18cm\Rightarrow R=\frac{9}{\pi }cm$

Perimeter of lower bottom = 6 cm

$\Rightarrow 2\pi r=6\Rightarrow r=\frac{3}{\pi }cm$

Curved S.A. of frustum = $\pi l[R+r]$

$=\pi \times 4\times [\frac{9}{\pi }+\frac{3}{\pi }]$

$=\pi \times 4\times \frac{12}{\pi }$

= 48 cm${}^2$