Question

find the volume of a cone with a base diameter of 12 in and a height of 11 in. 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 \(d = 12\) in. The radius \(r=\frac{d}{2}\), so \(r=\frac{12}{2}=6\) in.

Step2: Use the cone - volume formula

The volume formula of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Given \(\pi = 3.14\), \(r = 6\) in, and \(h = 11\) in.
Substitute the values into the formula: \(V=\frac{1}{3}\times3.14\times6^{2}\times11\).
First, calculate \(6^{2}=36\). Then \(V=\frac{1}{3}\times3.14\times36\times11\).
Since \(\frac{1}{3}\times36 = 12\), the formula becomes \(V=3.14\times12\times11\).
\(3.14\times12 = 37.68\), and then \(V=37.68\times11\).
\(37.68\times11=414.48\).

Answer:

\(414.48\) cubic inches