Question

find the volume of a cone with a height of 8 yd and a base diameter of 6 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 \(d = 6\) yd. The radius \(r=\frac{d}{2}\), so \(r=\frac{6}{2}=3\) yd.

Step2: Use the cone - volume formula

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Given \(h = 8\) yd, \(r = 3\) yd, and \(\pi=3.14\).
Substitute the values into the formula: \(V=\frac{1}{3}\times3.14\times3^{2}\times8\).
First, calculate \(3^{2}=9\). Then the expression becomes \(V=\frac{1}{3}\times3.14\times9\times8\).
Since \(\frac{1}{3}\times9 = 3\), the formula simplifies to \(V=3.14\times3\times8\).
Calculate \(3\times8 = 24\), then \(V=3.14\times24\).
\(V = 75.36\)

Answer:

\(75.36\) cubic yards