Question

find the volume of a right circular cone that has a height of 9.1 cm and a base with a circumference of 13.3 cm. round your answer to the nearest tenth of a cubic centimeter.

Explanation:

Step1: Find the radius from circumference

The formula for the circumference of a circle is \( C = 2\pi r \). We know \( C = 13.3 \) cm, so we solve for \( r \):
\( r=\frac{C}{2\pi}=\frac{13.3}{2\pi} \approx \frac{13.3}{6.2832} \approx 2.12 \) cm.

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 \( r \approx 2.12 \) cm and \( h = 9.1 \) cm. Substitute these values:
\( V=\frac{1}{3}\pi(2.12)^{2}(9.1) \)
First, calculate \( (2.12)^{2}=4.4944 \). Then:
\( V=\frac{1}{3}\pi(4.4944)(9.1) \approx \frac{1}{3}\pi(40.899) \approx \frac{128.47}{3} \approx 42.8 \) \( \text{cm}^3 \).

Answer:

\( 42.8 \)