Question

Question 8
If the triangle ABC in the above question is revolved about the side 5cm, then find the volume of the solid so obtained.
Find also the ratio of the volumes of the two solids obtained in Questions 7 and 8.

Answer 1

When a right-angled $\Delta ABC$ is revolved about its side 5 cm, a cone will be formed;
Having radius (r) as 12 cm, height (h) as 5 cm and slant height (l) as 13 cm.
Volume of the cone $=\frac{1}{3}\pi r^{2}h$
$=[\frac{1}{3}\times \pi \times (12{)}^2\times 5]c{m}^3$
$=240\pi c{m}^3$
Therefore, the volume of the cone so formed is $240\pi c{m}^3$.
Required ratio $=\frac{100\pi }{240\pi }$
$=\frac{5}{12}=5:12$