Question

The volume of a cone is 27∏ and the radius is 3. Can you find the length of the height?

My teacher requires work if it is not too much of a hassle please SHOW WORK!!!! thank you for helping.

Answer 1

The height is `9` units

Explanation:

The volume of the cone is given as `27pi` (unknown) cubic units.
You can make it a big cone that you can walk into and use `m^3`
or a small cone sitting on your table and use `cm^3`

The volume of a cone is: `V = pir^2 (h/3)`

Then: `27pi = pi(3)^2 (h/3)`

`27pi = pi(3)h`

`9pi = pih`

`h = 9` units

If you started with the big cone, the height is `9m` or `30ft`,
and if you decided on the small cone, the height is `9cm` or `3.5` inches.