Question

find the volume of a right circular cone that has a height of 14.9 cm and a base with a circumference of 2.9 cm. round your answer to the nearest tenth of a cubic centimeter.

Explanation:

Step1: Find the radius from the circumference

The formula for the circumference of a circle is \( C = 2\pi r \), so we can solve for \( r \): \( r=\frac{C}{2\pi} \). Given \( C = 2.9 \) cm, then \( r=\frac{2.9}{2\pi}\approx\frac{2.9}{6.2832}\approx0.4615 \) cm.

Step2: Use the cone volume formula

The volume \( V \) of a right circular cone is given by \( V=\frac{1}{3}\pi r^{2}h \). We know \( r\approx0.4615 \) cm and \( h = 14.9 \) cm. Substitute these values: \( V=\frac{1}{3}\pi(0.4615)^{2}(14.9) \). First, calculate \( (0.4615)^{2}\approx0.2130 \). Then, \( \frac{1}{3}\pi\times0.2130\times14.9\approx\frac{1}{3}\times3.1416\times0.2130\times14.9 \). Calculate \( 3.1416\times0.2130\approx0.6702 \), then \( 0.6702\times14.9\approx9.986 \), and finally \( \frac{9.986}{3}\approx3.329 \). Rounding to the nearest tenth gives \( 3.3 \) cubic centimeters.

Answer:

\( 3.3 \) cubic centimeters