Question

the height of a cone is twice the radius of its base. what expression represents the volume of the cone, in cubic units? o $\frac{2}{3}pi x^{3}$ o $\frac{4}{3}pi x^{2}$ o $2pi x^{3}$ o $4pi x^{3}$

Explanation:

Step1: Recall volume formula

The volume formula for a cone is $V = \frac{1}{3}\pi r^{2}h$, where $r$ is the radius of the base and $h$ is the height.

Step2: Substitute given values

Given that $r = x$ and $h=2x$. Substitute these into the formula: $V=\frac{1}{3}\pi(x)^{2}(2x)$.

Step3: Simplify the expression

$V=\frac{1}{3}\pi\times x^{2}\times2x=\frac{2}{3}\pi x^{3}$.

Answer:

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