Question

If the volume of a right circular cone of height 9 cm is 48 `pi`  cm³, find the diameter of its base.

Answer 1

The formula of the volume of a cone with base radius ‘r’ and vertical height ‘h’ is given as

Volume of cone = `1/3 pi r^2 h`

It is given that the height of the cone is ‘h’ = 9 cm and that the volume of the cone is 48π cm³

We can now find the radius of base ‘r’ by using the formula for the volume of a cone.

`r^2 =(3( " Volume of the cone" ))/(pih)`

`r^2 = (3(48 pi))/(pi(9))`

`r^2 = 16`

r = 4

Hence the radius of the base of the cone with given dimensions is ‘r’ = 4 cm.

The diameter of base is twice the radius of the base.

Hence the diameter of the base of the cone is  8 cm  .