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.

When right-angled \(\triangle{ABC}\) is revolved about its side 12 cm, a cone With height (h) as 12 cm, radius (r) as 5 cm, and slant height (l) 13 cm will be formed.

Now, thus, we know that,
Volume of cone
= \(\frac{1}{3} {\pi} {r}^2 h\)
= \(\frac{1}{3} × {\pi} × {5}^2 × 12\) \({cm}^3\)
= \(\frac{1}{3} × 300 × {\pi}\) \({cm}^3\)
\(= 100 {\pi}\) \({cm}^3\)

Therefore, the volume of the cone so formed is \(100 {\pi}\) \({cm}^3\)