Question

the height of a cylinder is twice the radius of its base. what expression represents the volume of the cylinder, in cubic units? 4πx² 2πx³ πx² + 2x 2 + πx³

Explanation:

Step1: Recall volume formula

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

Step2: Identify radius and height

Given that the radius $r = x$ and the height $h=2x$.

Step3: Substitute values into formula

Substitute $r = x$ and $h = 2x$ into $V=\pi r^{2}h$, we get $V=\pi\times x^{2}\times2x$.

Step4: Simplify the expression

Using the rule of exponents $a^{m}\times a^{n}=a^{m + n}$, we have $V = 2\pi x^{3}$.

Answer:

$2\pi x^{3}$