Question

find the volume of a cone with a height of 9 yd and a base diameter of 8 yd. use the value 3.14 for π, and do not do any rounding. be sure to include the correct unit in your answer.

Explanation:

Step1: Find the radius of the base

The diameter $d = 8$ yd, and the radius $r=\frac{d}{2}=\frac{8}{2}=4$ yd.

Step2: Recall the volume formula for a cone

The volume formula of a cone is $V=\frac{1}{3}\pi r^{2}h$.

Step3: Substitute the values into the formula

We have $\pi = 3.14$, $r = 4$ yd and $h=9$ yd. So $V=\frac{1}{3}\times3.14\times4^{2}\times9$.
First, calculate $4^{2}=16$. Then $V=\frac{1}{3}\times3.14\times16\times9$.
$\frac{1}{3}\times9 = 3$, so $V=3.14\times16\times3$.
$16\times3=48$, and $V = 3.14\times48=150.72$ yd³.

Answer:

$150.72$ yd³