Question

find the volume of a right circular cone that has a height of 9.5 in and a base with a circumference of 3.4 in. round your answer to the nearest tenth of a cubic inch.

Explanation:

Step1: Find the radius from circumference

The formula for the circumference of a circle is \( C = 2\pi r \). We know \( C = 3.4 \) in, so we solve for \( r \):
\( r=\frac{C}{2\pi}=\frac{3.4}{2\pi}\approx\frac{3.4}{6.2832}\approx0.541 \) in.

Step2: Calculate the volume of the cone

The formula for the volume of a right circular cone is \( V = \frac{1}{3}\pi r^{2}h \). We know \( h = 9.5 \) in and \( r\approx0.541 \) in. Substitute these values:
\( V=\frac{1}{3}\pi(0.541)^{2}(9.5) \)
First, calculate \( (0.541)^{2}\approx0.2927 \). Then:
\( V=\frac{1}{3}\pi(0.2927)(9.5)\approx\frac{1}{3}\pi(2.7807)\approx\frac{8.738}{3}\approx2.9 \) cubic inches.

Answer:

\( \approx 2.9 \) cubic inches