find the volume of a right circular cone that has a height of 9.1 m and a base with a circumference of 12.1…

find the volume of a right circular cone that has a height of 9.1 m and a base with a circumference of 12.1 m. round your answer to the nearest tenth of a cubic meter.

find the volume of a right circular cone that has a height of 9.1 m and a base with a circumference of 12.1 m. round your answer to the nearest tenth of a cubic meter.

Answer

Explanation:

Step1: Find base radius from circumference

The circumference formula is $C=2\pi r$. Solve for $r$: $r=\frac{C}{2\pi}=\frac{12.1}{2\pi}\approx1.926$ m

Step2: Calculate cone volume

Volume formula for cone: $V=\frac{1}{3}\pi r^2 h$ Substitute $r\approx1.926$ m, $h=9.1$ m: $V=\frac{1}{3}\pi(1.926)^2(9.1)\approx\frac{1}{3}\pi(3.71)(9.1)\approx\frac{1}{3}\times106.5\approx35.5$

Answer:

$35.5$ cubic meters