Question

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

Explanation:

Step1: Recall cylinder volume formula

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

Step2: Identify given values

From the diagram, $r = x$ and $h = 2x$.

Step3: Substitute values into formula

Substitute $r=x$, $h=2x$ into $V = \pi r^2 h$:
$V = \pi (x)^2 (2x)$

Step4: Simplify the expression

Multiply the terms:
$V = \pi \cdot x^2 \cdot 2x = 2\pi x^3$

Answer:

$\boldsymbol{2\pi x^3}$ (corresponding to the second option)