Question

find the volume of a right circular cone that has a height of 19.2 ft and a base with a circumference of 7.6 ft. round your answer to the nearest tenth of a cubic foot.

Explanation:

Step1: Find the radius of the base

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=7.6\) ft, we can solve for \(r\):
\(r=\frac{C}{2\pi}=\frac{7.6}{2\pi}\approx\frac{7.6}{2\times3.14}\approx1.21\) ft.

Step2: Calculate the volume of the cone

The formula for the volume of a cone is \(V=\frac{1}{3}\pi r^{2}h\). Substitute \(r = 1.21\) ft and \(h = 19.2\) ft:
\(V=\frac{1}{3}\times\pi\times(1.21)^{2}\times19.2\)
First, calculate \((1.21)^{2}=1.4641\).
Then, \(V=\frac{1}{3}\times\pi\times1.4641\times19.2\)
\(V=\frac{1}{3}\times\pi\times28.11072\)
\(V\approx\frac{1}{3}\times3.14\times28.11072\)
\(V\approx\frac{88.2676608}{3}\approx29.4\) ft³.

Answer:

\(29.4\) ft³