Question

The curved surface area of the frustum of a cone is $180$ sq. cm and the circumference of its circular bases are $18$ cm and $6$ cm respectively. Find the slant height of the frustum of a cone (in cm).

Answer 1

Curved Surface area of a frustum of a cone $=\pi l(r_1+r_2)$ where $l$ is the slant height,

$r_1$ and $r_1$ are the radii of the lower and upper ends of a frustum of a cone.
Circumference of the lower circular base $=2\pi r_1=18$
$\Rightarrow r_1=\frac{9}{\pi }$ cm
Circumference of the upper circular base $=2\pi r_2=6$
$\Rightarrow r_2=\frac{6}{\pi }$ cm
Given, curved Surface area of the frustum of a cone $=\pi \times l\times (\frac{9}{\pi }+\frac{6}{\pi })=180$
$l=12$ cm