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

Explanation

Let `triangleABC` be right angled at B with AB = 5cm, BC = 12 cm and AC = 13cm.
On revolving `triangleABC` about the side BC = 12c, we obtain a right circular cone of radius 5 cm and height 12 cm

Volume of the cone so formed
`= {(1)/(3)pi xx (5)^(2) xx 12} cm^(3)`
`= (100pi) cm^(3) = V_(1)` (say)
On revolving `triangleABC` about the side AB = 5cm, we obtain a right circular cone of radius 12 cm and height 5 cm

Volume of the cone so formed
`= {(1)/(3) pi xx (12)^(2) xx 5} cm^(3)`
`= (240pi) cm^(3) = V_(2)` (say)
`:. (V_(1))/(V_(2)) = (100pi)/(240pi) = (5)/(12) rArr V_(1) : V_(2) + 5 : 12`