Question

find the volume of a cone with a base diameter of 9 yd and a height of 6 yd. write the exact volume in terms of π, and be sure to include the correct unit in your answer.

Explanation:

Step1: Find the radius

The diameter $d = 9$ yd, and the radius $r=\frac{d}{2}=\frac{9}{2}$ yd.

Step2: Use the cone - volume formula

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$. Substitute $r = \frac{9}{2}$ yd and $h = 6$ yd into the formula.
$V=\frac{1}{3}\pi(\frac{9}{2})^{2}\times6$.
First, calculate $(\frac{9}{2})^{2}=\frac{81}{4}$. Then, $\frac{1}{3}\pi\times\frac{81}{4}\times6$.
$\frac{1}{3}\times6 = 2$, so $V = 2\times\frac{81}{4}\pi$.
$2\times\frac{81}{4}=\frac{81}{2}$.

Answer:

$\frac{81}{2}\pi$ yd³