Question

find the volume of a cone with a base radius of 6 in and a height of 10 in. write the exact volume in terms of π, and be sure to include the correct unit in your answer.

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 of the base and $h$ is the height.

Step2: Substitute given values

Given $r = 6$ in and $h=10$ in. Substitute into the formula: $V=\frac{1}{3}\pi\times(6)^{2}\times10$.

Step3: Simplify the expression

First, calculate $(6)^{2}=36$. Then, $\frac{1}{3}\times36\times10\pi = 12\times10\pi=120\pi$ in$^{3}$.

Answer:

$120\pi$ in$^{3}$