Question

A spherical cannon ball, $28\text{cm}$ in diameter is melted and cast into a right circular conical mould, the base of which is $35\text{cm}$ in diameter. Find the height of the cone.

Answer 1

Radius of cannon ball $=14\text{cm}$

Volume of cannon ball$=\frac{4\pi r^3}{3}$

Radius of conical mould$=\frac{35}{2}\text{cm}$

Volume of conical mould$=\frac{1}{3}\pi r^{2}h$

Since material of cannon ball is used to make right circular mould, Hence

$⟹\begin{array}{c}Volumeofsphere=volumeofcone\\ \frac{4}{3}\pi r^3=\frac{1}{3}\pi r^{2}h\\ 4\times 14\times 14\times 14=\frac{35}{2}\times \frac{35}{2}\times h\\ h=\frac{4\times 2\times 2\times 14\times 14\times 14}{35\times 35}\\ h=35.84\text{cm}\end{array}$