Question

find the volume of a right circular cone that has a height of 14.7 ft and a base with a circumference of 13 ft. round your answer to the nearest tenth of a cubic foot. answer attempt 1 out of 3 ft³ submit answer

Explanation:

Step1: Find the radius of the base

The formula for the circumference of a circle is \(C = 2\pi r\). Given \(C=13\) ft, we can solve for \(r\):

$$r=\frac{C}{2\pi}=\frac{13}{2\pi}$$

$$r\approx\frac{13}{2\times3.14}\approx\frac{13}{6.28}\approx2.07$$

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 \(r = 2.07\) ft and \(h = 14.7\) ft:

$$V=\frac{1}{3}\times\pi\times(2.07)^{2}\times14.7$$

$$V=\frac{1}{3}\times\pi\times4.2849\times14.7$$

$$V=\frac{1}{3}\times\pi\times63.088$$

$$V\approx\frac{1}{3}\times3.14\times63.088$$

$$V\approx\frac{198.196}{3}\approx66.1$$

Answer:

\(66.1\)