Question

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

Answer 1

Given:

$\Rightarrow$$r=5$cm, $l=13$cm, $h=12$cm

$\Rightarrow$Volume $=\frac{1}{3}\pi r^{2}h=\frac{1}{3}\pi \times 5\times 5\times 12=100\pi$cm${}^3$

$\Rightarrow$$r=12$, $h=5$cm, $l=13$cm

$\Rightarrow$Volume $=\frac{1}{3}\pi \times 12\times 12\times 5=240\pi$cm${}^3$

$\Rightarrow$Ratio $=\frac{100\pi }{240\pi }=\frac{10}{24}=\frac{5}{12}$

$\Rightarrow$$5:12$