Question

volume of a cone level 1
question
find the volume of a right circular cone that has a height of 16 in and a base with a circumference of 4.5 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 \( C = 2\pi r \). Given \( C = 4.5 \) in, we solve for \( r \):
\( r=\frac{C}{2\pi}=\frac{4.5}{2\pi} \approx \frac{4.5}{6.2832} \approx 0.716 \) in.

Step2: Calculate the volume of the cone

The formula for the volume of a cone is \( V=\frac{1}{3}\pi r^{2}h \). We know \( h = 16 \) in and \( r\approx0.716 \) in. Substitute these values:
\( V=\frac{1}{3}\pi(0.716)^{2}(16) \)
First, calculate \( (0.716)^{2}\approx0.512656 \).
Then, \( \frac{1}{3}\pi(0.512656)(16)\approx\frac{1}{3}\pi(8.202496) \approx\frac{25.769}{3}\approx8.59 \) in³.

Answer:

\( 8.6 \) (rounded to the nearest tenth)