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

Answer 1

$\bf \textit{volume of a cone}\\\\ V=\cfrac{\pi r^2 h}{3}~~ \begin{cases} r=radius\\ h=height\\ -----\\ r=3\\ h=2a \end{cases}\implies V=\cfrac{\pi (3^2)(2a)}{3}\implies V=6a\pi$

Answer 2

Answer:

C. $6a \pi\text{ units}^3$  

Step-by-step explanation:

We have been given that a cone has a radius of 3 and a height given by the expression 2a.

To find the volume of our given cone we will use volume of cone formula.

$\text{Volume of cone}=\frac{1}{3}*\pi r^2*h$

Upon substituting our given values in volume formula we will get,

$\text{Volume of cone}=\frac{1}{3}*\pi*3^2*2a$

$\text{Volume of cone}=\frac{1}{3}*\pi*9*2a$

$\text{Volume of cone}=\pi*3*2a$

$\text{Volume of cone}=6a\pi$

Therefore, the expression $6a \pi\text{ units}^3$ represents the volume of our given cone and option C is the correct choice.