Question

A right triangle $ABC$ with sides $5cm,12cm$ and $13cm$ is revolved about the side $12cm$.If the triangle $ABC$ is revolved about the side $5cm$, then find the volume of the solid so obtained. Find also the ratio of the volumes of the two solids obtained.

• A. $5:12$
• B. $12:5$
• C. $13:12$
• D. $5:11$

Answer 1

The correct option is A $5:12$

When the triangle is revolved around the side $12cm$, the solid obtained is a cone with height $12cm$, radius $5cm$ and slant height $13cm$

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

where, $r$ is the radius of the base of the cone and $h$ is the height.

Hence, volume of this cone $=\frac{1}{3}\times \pi \times 5^2\times 12=100\pi {cm}^3$

When the triangle is revolved around the side $5cm$, the solid obtained is a cone with height $5cm$, radius $12cm$ and slant height $13cm$

Hence, volume of this cone $=\frac{1}{3}\times \pi \times {12}^2\times 5=240\pi {cm}^3$

Ratio of the volumes $100\pi :240\pi =5:12$