Question

Curved surface area of a cone with base radius $20cm$ is $500\pi$ $c{m}^2$. Find the height of the cone.

Answer 1

$S_c=500\pi c{m}^2$
Base raidus $=20cm$
$S_c=\pi rl$
$\therefore 500\pi =\pi \times 20\times l$
$\therefore 500=20\times l$
$\therefore l=\frac{500}{20}$
$\therefore l=25cm$
$\because h^2+r^2=l^2$
$\therefore h^2=l^2-r^2$
$={25}^2-{20}^2$
$=625-400$
$=225$
$\therefore h=15cm$
Height of the cone is $15cm$.