A sphere of diameter 15.6 cm is melted and cast into a right circular cone of height 31.2 cm.
Question:

A sphere of diameter 15.6 cm is melted and cast into a right circular cone of height 31.2 cm. Find the diameter of the base of the cone.

Solution:

Radius of the sphere, = 7.8 cm
Height of the cone, h = 31.2 cm
Suppose that R cm is the radius of the cone.
Now, volume of the sphere = volume of the cone

$\Rightarrow \frac{4}{3} \pi r^{3}=\frac{1}{3} \pi R^{2} h$

$\Rightarrow 4 \times(7.8)^{3}=R^{2} \times 31.2$

$\Rightarrow R^{2}=\frac{4 \times 7.8 \times 7.8 \times 7.8}{31.2}=60.84$

$\Rightarrow R=7.8 \mathrm{~cm}$

∴ The diameter of the cone is 15.6 cm.