Question

The $C.S.A$ of a cone is $550c{m}^2$ whose height is $24cm$. Find the volume of the cone.

Answer 1

C.S.A of cone $=550{cm}^2$

$\therefore$ $\pi rl=550$

$\pi r\sqrt{h^2+r^2}=550$

$\frac{22}{7}\times r\sqrt{{576}^2+r^2}=550$

$r\sqrt{{576}^2+r^2}=\frac{550\times 7}{22}$

$r\sqrt{{576}^2+r^2}=175$

Now $r=7$ satisfies the equation

$\therefore$ Volume $=\frac{1}{3}\pi r^{2}h$

$\frac{1}{3}\times \frac{22}{7}\times 7\times 7\times 24$

$=154\times 8{cm}^3$

Volume $=1232{cm}^3$