Question

Find the volume of a right circular cone that has a height of 13.8 m and a base with a circumference of 15.8 m. Round your answer to the nearest tenth of a cubic meter.

Answer 1

Answer:

$V = 91.4m^3$

Step-by-step explanation:

Given

$h = 13.8$ --- height

$C = 15.8$ --- circumference

Required

Determine the volume

First, we calculate the radius of the base

The circumference is:

$C = 2\pi r$

$15.8 = 2\pi r$

Make r the subject

$r = \frac{15.8}{2\pi}$

$r = \frac{7.9}{\pi}$

The volume is then calculated as:

$V = \frac{1}{3}\pi r^2h$

This gives:

$V = \frac{1}{3} * \pi * (\frac{7.9}{\pi})^2 * 13.8$

$V = \pi * \frac{62.41}{\pi^2} * 4.6$

$V = \frac{62.41}{\pi} * 4.6$

$V = \frac{62.41* 4.6}{\pi}$

Take $\pi = 3.14$

$V = \frac{62.41* 4.6}{3.14}$

$V = 91.4m^3$ --- approximated