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Answer :
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 \(100 {\pi}\) \({cm}^3\)