Question

The slant height of the frustum of a cone is $4cm$, and the perimeter of its circular bases are $18cm$ and $6cm$. Find the curved surface area of the frustum of a cone.

Answer 1

Let $r_1$ and $r_2$ be the radii of the circular bases of the frustum, $l$ be the slant height, and $h$ be the height.

We have
Slant height, $l=4cm$

Perimeter of circular bases are given as

$2\pi r_1=18$ and, $2\pi r_2=6$

$\therefore 2\pi r_1=18$

$\Rightarrow 2\times \pi \times r_1=18$

$\Rightarrow r_1=18\times \frac{1}{2\pi }$

$\Rightarrow r_1=\frac{9}{\pi }$

And, $2\pi r_2=6$

$\Rightarrow r_2=\frac{6}{2\pi }$

$\Rightarrow r_2=\frac{3}{\pi }$

$\Rightarrow l=4cm,r_1=\frac{9}{\pi },r_2=\frac{3}{\pi }$

Curved surface area $=\pi (r_1+r_2)l=\pi (\frac{9}{\pi }+\frac{3}{\pi })\times 4{cm}^2=48{cm}^2$