Question

A right triangle ABC with sides $5cm$, $12cm$ and $13cm$ is revolved about the side $12cm$. Find the volume of the solid so obtained.

Answer 1

The volume of the cone is obtained as follows.

Solid so obtained is a cone with $r=5,h=12$

volume$=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}$

$$\begin{gathered} =\frac{\mathrm{\pi }}{3}\times 25\times 12 \\ =100\mathrm{\pi }{\mathrm{cm}}^3 \end{gathered}$$

Therefore, volume of the cone is $100\mathrm{\pi }{\mathrm{cm}}^3$