Question

A hemisphere of lead of radius 9 cm is cast into a right circular cone of height 72 cm. Find the radius of the base of the cone.

Answer 1

Radius of the hemisphere = 9 cm
Height of the right circular cone = 72 cm
Suppose that the radius of the base of the cone is r cm.
Volume of the hemisphere = volume of the cone

$$\begin{gathered} \Rightarrow \frac{2}{3}\mathrm{\pi }\times 9^3=\frac{1}{3}\mathrm{\pi }\times r^2\times 72 \\ \Rightarrow r^2=\frac{2\times 9\times 9\times 9}{72}=\frac{81}{4} \\ \Rightarrow r\mathit{}=\frac{9}{2}=4.5\mathrm{cm} \end{gathered}$$

∴ The radius of the base of the cone is 4.5 cm.