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.

Question

asked Apr 9, 2022 99.9k views

1 Answer

Onelaview · Answer 1 · 2022-04-15T20:35:24+0000

Answer:

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