Question

volume of a cone level 1
score:5/15 penalty:1 off
question
find the volume of a right circular cone that has a height of 13 in and a base with a circumference of 5.1 in. round your answer to the nearest tenth of a cubic inch.
answer attempt 1 out of 2
in³
submit answer
show examples

Explanation:

Step1: Find the radius from circumference

The formula for the circumference of a circle is \( C = 2\pi r \). We know \( C = 5.1 \) in, so we solve for \( r \):
\( r=\frac{C}{2\pi}=\frac{5.1}{2\pi}\approx\frac{5.1}{6.2832}\approx0.812 \) in.

Step2: Use the cone volume formula

The volume of a cone is \( V=\frac{1}{3}\pi r^{2}h \). We know \( h = 13 \) in and \( r\approx0.812 \) in. Substitute these values:
\( V=\frac{1}{3}\pi(0.812)^{2}(13) \)
First, calculate \( (0.812)^{2}\approx0.659 \). Then:
\( V=\frac{1}{3}\pi(0.659)(13)\approx\frac{1}{3}\pi(8.567)\approx\frac{26.91}{3}\approx8.97 \)
Round to the nearest tenth: \( V\approx9.0 \) cubic inches.

Answer:

\( 9.0 \)