Question

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

13em 12cm 

Answer 1

Given that a right triangle ABC with sides $5cm,12cm$ and $13cm$ is revolved about the side $12cm$

So, after revolution a cone will be formed, such that

Radius of cone $\left(r\right)=5cm$

Height of cone $\left(h\right)=12cm$

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

$$\begin{gathered} =\frac{1}{3}\times \mathrm{\pi }\times 5\times 5\times 12 \\ =\frac{12\times \mathrm{\pi }\times 5\times 5}{3} \\ \mathrm{V}=100\mathrm{\pi }{\mathrm{cm}}^3 \end{gathered}$$

Therefore, Volume of the cone$=100\mathrm{\pi }$ $c{m}^3$