a cone has a radius of 3 and a height given by the expression 2a. which expression represents the volume of…

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 and $h$ is the height.

Step2: Substitute given values

Given $r = 3$ and $h=2a$, substitute into the formula: $V=\frac{1}{3}\pi\times3^{2}\times2a$.

Step3: Simplify the expression

First, calculate $3^{2}=9$. Then $V=\frac{1}{3}\pi\times9\times2a$. $\frac{1}{3}\times9 = 3$, so $V = 3\pi\times2a=6a\pi$.

Answer:

$6a\pi$ units$^{3}$