A right-angled triangle whose sides are 6 cm, 8 cm and 10 cm is revolved about the sides containing the right angle in two ways. Find the difference in volumes of the two solids so formed.

#### Solution

Three sides of a triangle are 6 cm, 8 cm and 10 cm.

**Case (i): **If the triangle is revolved about the side 6 cm, the cone will be formed with radius 6 cm and height 8 cm.

Volume of the cone = `1/3 pi"r"^2"h"` cu. units

= `1/3 xx pi xx 6 xx 6 xx 8`

= 96π cm^{3 }

**Case (ii):** If the triangle is revolved about the side 8 cm, the cone will be formed with radius 8 cm and height 6 cm.

Volume of the cone = `1/3 xx pi xx 8 xx 8 xx 6`

= 128π cm^{3 }

Difference in volume of the two solids

= (128π – 96π) cm^{3}

= 32π cm^{3}

= `32 xx 22/7` cm^{3 }

= 100.57 cm^{3 }

The difference in the volume of the two solids = 100.57 cm^{3}