Question

A spherical cannon ball, 28 cm in diameter, is melted and recast into a right circular conical mould with base diameter of 35 cm. Find the height of the cone.

Answer 1

Diameter of cannon ball = 28 cm
Radius of the cannon ball = 14 cm

Volume of ball $=\frac{4}{3}{\mathrm{\pi r}}^3=\frac{4}{3}\mathrm{\pi }\times {\left(14\right)}^3{\mathrm{cm}}^3$

Diameter of base of cone = 35 cm

Radius of base of cone $=\frac{35}{2}cm$
Let the height of the cone be h cm.

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

From the above results and from the given conditions,
Volume of ball = Volume of cone

$$\begin{gathered} \text{Or},\frac{4}{3}\mathrm{\pi }\times {\left(14\right)}^3=\frac{1}{3}\mathrm{\pi }\times {\left(\frac{35}{2}\right)}^2\times \mathrm{h} \\ \Rightarrow \mathrm{h}=\frac{\frac{4}{3}\mathrm{\pi }\times {\left(14\right)}^3}{\frac{1}{3}\mathrm{\pi }\times {\left(\frac{35}{2}\right)}^2}=\frac{4\times 14\times 14\times 14\times 2\times 2}{35\times 35}=35.84\mathrm{cm} \end{gathered}$$