Question

If the triangle $ABC$ 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 .

Answer 1

R.E.F image

$△ABC$ is right angle at B

AC is hypotenuse ie; AC = 13cm

AB = 12cm & BC = 5cm

we revolve $△ABC$ and we get a cone

by cone radius r = 12 cm

height h = 5 cm

volume of cone $\frac{1}{3}\pi r^{2}h$

$=(\frac{1}{3}\times \pi \times 12\times 12\times 5)c{m}^3$

$=240\pi c{m}^3$

Ratio of volume $=\frac{volumein{Q}_7}{volumein{Q}_8}=\frac{100\pi }{240\pi }=\frac{5}{12}$

ratio of volume $=5:12$