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.

Answer 1

Radius of the sphere, r = 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
$$\begin{gathered} \Rightarrow \frac{4}{3}\mathrm{\pi }{r}^3=\frac{1}{3}\mathrm{\pi }{R}^{\mathit{2}}h \\ \Rightarrow 4\times {\left(7.8\right)}^3=R^2\times 31.2 \\ \Rightarrow R^{\mathit{2}}=\frac{4\times 7.8\times 7.8\times 7.8}{31.2}=60.84 \\ \Rightarrow R=7.8\mathrm{cm} \end{gathered}$$

∴ The diameter of the cone is 15.6 cm.