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

Radius of hemisphere $\left(r\right)=7cm\therefore Volume=\frac{2}{3}\pi r^3=\frac{2}{3}\times \pi \times 7\times 7\times 7c{m}^3=\frac{686}{3}\pi c{m}^{3}NowVolumeofcone=\frac{686}{3}\pi c{m}^3$
$Heightofcone=49cm\therefore Radius=\sqrt{\frac{Volume\times 3}{\pi h}}=\sqrt{\frac{676\pi \times 3}{3\times \pi \times 49}}=\sqrt{\frac{686}{49}}=\sqrt{14}cm=3.74$