Question

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

Answer 1

when a right triangle ABC is revolved about the side 5cm, a cone is formed as shown in the above figure, where

radius r = 12 cm

height h = 5 cm

and slant height l = 13cm

Now, volume of the cone = πr2 h/3

                                     = {π(12)2 * 5}/3

                                     = {π *12 * 12 * 5}/3

                                     = π *12 * 4 * 5

                                     = 240π

Case 2: when a right triangle ABC is revolved about the side 12cm, a cone is formed as shown in the above figure, where

radius r = 5 cm

height h = 12 cm

and slant height l = 13cm

Now, volume of the cone = πr2 h/3

                                     = {π 52 * 12}/3

                                     = {π *5 * 5 * 12}/3

                                     = π *25 * 4

                                     = 100π

Now, required ratio = 100π/240π = 100/240 = 10/24 = 5/12 = 5 : 12

Answer 2

height = 12 cm , radius= 5 cm

the solid formed a cone whose volume = 1/3$\pi$r²h

1/3* $\pi$* 5*5*12

=100$\pi$cm²