Question

find the volume of a cone with a base diameter of 8 yd and a height of 9 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

The diameter \(d = 8\) yd. The radius \(r=\frac{d}{2}\), so \(r=\frac{8}{2}=4\) yd.

Step2: Use the cone - volume formula

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Substitute \(\pi = 3.14\), \(r = 4\) yd, and \(h = 9\) yd into the formula.
First, calculate \(r^{2}\): \(r^{2}=4^{2}=16\).
Then, calculate \(\pi r^{2}h\): \(3.14\times16\times9=3.14\times144 = 452.16\).
Finally, calculate \(\frac{1}{3}\pi r^{2}h\): \(V=\frac{1}{3}\times452.16 = 150.72\).

Answer:

\(150.72\) cubic yards