Question

find the volume of a right circular cone that has a height of 17 ft and a base with a circumference of 5 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 \(C = 5\) ft, we can solve for \(r\):
\(r=\frac{C}{2\pi}=\frac{5}{2\pi}\) 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 \(r = \frac{5}{2\pi}\) and \(h = 17\) into the formula:

$$
LATEXBLOCK0
$$

Now, calculate \(\frac{425}{12\pi}\approx\frac{425}{12\times3.14}\approx\frac{425}{37.68}\approx11.3\)

Answer:

\(11.3\)