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

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.

Solution:

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

$\Rightarrow \frac{2}{3} \pi \times 9^{3}=\frac{1}{3} \pi \times r^{2} \times 72$

$\Rightarrow r^{2}=\frac{2 \times 9 \times 9 \times 9}{72}=\frac{81}{4}$

$\Rightarrow r=\frac{9}{2}=4.5 \mathrm{~cm}$

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

 

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