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

`V = 91.4m^3`

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 = (15.8)/(2\pi)`

`r = (7.9)/(\pi)`

The volume is then calculated as:

`V = (1)/(3)\pi r^2h`

This gives:

`V = (1)/(3) * \pi * ((7.9)/(\pi))^2 * 13.8`

`V = \pi * (62.41)/(\pi^2) * 4.6`

`V = (62.41)/(\pi) * 4.6`

`V = (62.41* 4.6)/(\pi)`

Take
`\pi = 3.14`

`V = (62.41* 4.6)/(3.14)`

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