Question

Find the volume of a right circular cone that has a height of 5.7 m and a base with a circumference of 2.3 m. Round your answer to the nearest tenth of a cubic meter.

Answer 1

Volume of the cone is approximately 0.8 cubic meters

Explanation:

Recall that the volume of a circular cone is defined by:

`V=\pi R^2\,(H)/(3)`

where R is the radius of the cone's base, and H the cone's height. Since we have the information of the height H (5.7 m) we just need to find the radius R. We can do such by using the other piece of information: the circumference of its base.

The circumference of a circle is the product:
`2\,\pi\,R`

So by knowing the circumference's length (2.3 m) we can solve for the radius R:

`2.3\,m=2\,\pi\,R\\R=(2.3)/(2\,\pi) \,m\\R=0.366\,m`

We can now use this result in the formula for the volume:

`V=\pi ^2\,(H)/(3)\\V=\pi (0.366)^2\,(5.7)/(3)\,m^3\\V=0.7995868\, m^3`which can be rounded to the nearest tenth as:

`V=0.8\,m^3`