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

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

#### Solution

(i)

When right-angled ΔABC 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.

`"Volume of cone "=1/3πr^2h`

`=[1/3xx pi xx(5)^2xx12]cm^3`

= 100π cm^{3}

Therefore, the volume of the cone so formed is 100π cm^{3}.

(ii)

When right-angled ΔABC 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 cone "=1/3pir^2h`

`=[1/3xx pi xx(12)^2xx5]cm^3`

= 240π cm^{3}

Therefore, the volume of the cone so formed is 240π cm^{3}.

`"Required ratio "= (100pi)/(240pi) = 5/12 = 5:12`