Question

The height of a cone is twice the radius of its base.2xXWhat expression represents the volume of the cone, incubic units?OOO-7x³x²27x³47x³

Answer 1

Given:

Height of cone = twice the radius of the base.

Let's determine the expression which represents the volume of the cone.

Apply the formula for volume of a cone:

$V=\frac{\pi r^2h}{3}$

Where:

• V is the volume

,

• r is the radius

,

• h is the height.

Since the height is twice the radius, we have:

h = 2r

In this case, since x represents the radius, the equation will be:

r = x

h = 2x

Substitute 2x for h and substitute x for r in the formula:

$\begin{gathered} V=\frac{\pi x^22x}{3} \\ \\ V=\frac{2}{3}\pi x^2x \\ \\ V=\frac{2}{3}\pi x^3 \end{gathered}$

Therefore, the expression which represents the volume of the cone is:

$\frac{2}{3}\pi x^3$

• ANSWER:

$\frac{2}{3}\pi x^3$