Question

A solid metal cone with base radius 12 cm and height 24 cm is melted to form solid spherical balls of diameter 6 cm each. Find the number of balls formed.

Answer 1

Radius of cone = 12 cm
Height of cone = 24 cm
Volume of the metallic cone$=\frac{1}{3}\mathrm{\pi }{r}^{2}h$
$=\frac{1}{3}\mathrm{\pi }\times {\left(12\right)}^2\times 24$

Radius of spherical ball = $\frac{6}{2}\mathrm{cm}=3\mathrm{cm}$

Volume of each spherical ball$=\frac{4}{3}\mathrm{\pi }{\mathrm{r}}^3$
$=\frac{4}{3}\mathrm{\pi }\times {\left(3\right)}^3$

Number of balls formed$=\frac{\text{Volume of the metallic cone}}{\mathrm{Volume}\mathrm{of}\mathrm{each}\mathrm{spherical}\mathrm{ball}}$

$$\begin{gathered} =\frac{\mathrm{\pi }\times 12\times 12\times 24\times 3}{3\times 4\times \mathrm{\pi }\times 3\times 3\times 3} \\ =32 \end{gathered}$$