Question

find the volume of a cone with a base diameter of 12 m and a height of
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 \(d = 12\) m. The radius \(r=\frac{d}{2}\), so \(r=\frac{12}{2}=6\) m.

Step2: Use the cone - volume formula

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Given \(\pi = 3.14\), \(r = 6\) m, and \(h = 12\) m.
Substitute the values into the formula:
\(V=\frac{1}{3}\times3.14\times6^{2}\times12\)
First, calculate \(6^{2}=36\).
Then, \(\frac{1}{3}\times3.14\times36\times12=( \frac{1}{3}\times36)\times3.14\times12\)
Since \(\frac{1}{3}\times36 = 12\), the formula becomes \(12\times3.14\times12\)
\(12\times12 = 144\), so \(V=144\times3.14\)
\(V = 452.16\)

Answer:

\(452.16\space m^{3}\)