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 cm3
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 cm3
Difference in volume of the two solids
= (128π – 96π) cm3
= 32π cm3
= `32 xx 22/7` cm3
= 100.57 cm3
The difference in the volume of the two solids = 100.57 cm3
