Answer in Brief

If the volume of a right circular cone of height 9 cm is 48 `pi` cm^{3}, find the diameter of its base.

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#### Solution

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 cm^{3}

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 .**

Concept: Volume of a Right Circular Cone

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