Question

The base diameter and the height of a cone are both equal to x units.Which expression represents the volume of the cone, in cubic units?

Answer 1

V = Πx³/12 units³

Explanation:

Volume of a cone = 1/3Πr²h where

r is the base radius of the cone and h is its height

If the base diameter and the height of a cone are both equal to x units, the radius of the cone will become;

radius = diameter/2 = x/2 units

Height = x units

Substituting the value of the radius and height into the volume of the cone, we have;

V = 1/3Π(x/2)² × x

V = 1/3Π(x³/4)

V = Πx³/12 units³

Therefore the volume of the cone, in cubic units is expressed as

V = Πx³/12 units³

Answer 2

`V=(1)/(3)\pi (x^4)/(8)\ units^3`

Explanation:

The volume of a cone has the following form:

`V=(1)/(3)\pi r^3h`

In this case we know that:

`r=(x)/(2)\ units` and
`h=x\ units`

Therefore the Volume is:

`V=(1)/(3)\pi ((x)/(2))^3(x)`

Finally the expression that represents the volume of the cone, in cubic units is:

`V=(1)/(3)\pi (x^4)/(8)\ units^3`