# 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.

Mar 7, 2017

The height is $9$ units

#### Explanation:

The volume of the cone is given as $27 \pi$ (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 $c {m}^{3}$

The volume of a cone is: $V = \pi {r}^{2} \left(\frac{h}{3}\right)$

Then: $27 \pi = \pi {\left(3\right)}^{2} \left(\frac{h}{3}\right)$

$27 \pi = \pi \left(3\right) h$

$9 \pi = \pi h$

$h = 9$ units

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