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

C.
`6a \pi\text{ units}^3`

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}=(1)/(3)*\pi r^2*h`

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

`\text{Volume of cone}=(1)/(3)*\pi*3^2*2a`

`\text{Volume of cone}=(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.