Question

A solid metallic sphere of diameter 21 cm is melted and recast into small cones of diameter 3.5 cm and height 3 cm each. Find the number of cones so formed.

Answer 1

Radius of sphere = $\frac{21}{2}\mathrm{cm}$
Volume of the metallic sphere$=\frac{4}{3}\mathrm{\pi }{\mathrm{r}}^3$
$=\left(\frac{4}{3}\mathrm{\pi }\times \frac{21}{2}\times \frac{21}{2}\times \frac{21}{2}\right){\text{cm}}^3$

Radius of cone = $\frac{3.5}{2}\mathrm{cm}$
Height of cone = 3 cm

Volume of each small cone$=\frac{1}{3}\mathrm{\pi }{r}^{2}h$
$=\left(\frac{1}{3}\mathrm{\pi }\times \frac{35}{20}\times \frac{35}{20}\times 3\right){\text{cm}}^3$

Number of cones$=\frac{\text{Volume of the metallic sphere}}{\text{Volume of each cone}}$

$$\begin{gathered} =\frac{4\times \mathrm{\pi }\times 21\times 21\times 3\times 20\times 20}{3\times 2\times 2\times 2\times \mathrm{\pi }\times 35\times 3\times 3\times 3} \\ =504 \end{gathered}$$