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

Hint:
When the triangle is revolved about the side 12 we get a cone with height 12 and radius 5cm .And the volume of the cone is obtained using the formula $\dfrac{1}{3}\pi {r^2}h{\text{cubic units}}$.

Complete step by step solution:
We are given a right angle triangle ABC.
We are given that the triangle revolves about the side 12 cm.

Hence, we get a cone with height 12 cm and radius 5 cm.
We know that the volume of the cone is given by the formula.
$ \Rightarrow \text{volume} = \dfrac{1}{3}\pi {r^2}{\text{h cubic}}{\text{ units}}$
Substituting the known values we get,
  $
   \Rightarrow \text{volume} = \dfrac{1}{3}\times\dfrac{{22}}{7} \times 5\times 5\times 12 \\
   \Rightarrow \text{volume} = \dfrac{{6600}}{{21}} \\
   \Rightarrow \text{volume} = 314.29{\text{c}{m^3}} \\
 $

Hence the volume of the cone is obtained.

Note:
Here the height of the cone depends on the side by which the triangle is revolved.
As we are asked for volume we used the the radius and height but if we are asked for the curved surface area or total surface area we may use the slant height which is 13 cm