Question

a cone has a radius of 3 and a height given by the expression 2a. which expression represents the volume of the cone?
○ 2aπ units³
○ 4a²π units³
○ 6aπ units³
○ 24aπ units³

Explanation:

Step1: Recall cone volume formula

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

Step2: Substitute given values

Substitute $r=3$, $h=2a$ into the formula:
$V = \frac{1}{3}\pi (3)^2 (2a)$

Step3: Simplify the expression

First calculate $(3)^2=9$, then $\frac{1}{3} \times 9 = 3$, then $3 \times 2a = 6a$:
$V = 6a\pi$

Answer:

6aπ units³ (Option C)