Question

A hemisphere made of lead of radius $7cm$ is cast into a right circular cone of height $49cm.$ Find the radius of the base of the cone.

Answer 1

Given: Radius of hemisphere $\left(r\right)=7cm$

$\therefore$ Volume of hemisphere $=\frac{2}{3}\pi r^3$

$=\frac{2}{3}\times \pi \times 7\times 7\times 7c{m}^3$

$=\frac{686}{3}\pi c{m}^3$

Now, Volume of hemisphere $=\frac{686}{3}\pi c{m}^3$

Height of cone $=49cm$

Volume of hemisphere $=$ Volume of cone [As hemisphere is casted into cone]

$\Rightarrow \frac{686}{3}\pi =\frac{1}{3}\pi r^{2}h$

$\Rightarrow 686=r^2\times 49$

$\Rightarrow \frac{686}{49}=r^2$

$\Rightarrow r=\sqrt{\frac{686}{49}}=\sqrt{14}cm=3.74cm$

Hence, the radius of cone is $3.74cm$