Answer:
Height = 7 meters
Step-by-step explanation:
Equation:
To work out the height, you need to know the formula for the volume of a cone which is:
[tex]V=\frac{1}{3} \pi r^2h[/tex]
Explaining variables:
[tex]\pi[/tex] - mathematical constant.
[tex]r[/tex] - radius of the cone
[tex]h[/tex] - height of the cone
[tex]V[/tex] - volume of the cone
Working out the height:
We are looking for the height, so let's re-arrange the equation.
[tex]h=\frac{3V}{\pi r^2}[/tex]
We are given the height, volume and diameter.
To work out the radius we have to know that [tex]d=2r[/tex]. So the radius is [tex]\frac{12}{2} =6[/tex] m.
Now let's put everything in the equation for the height to work it out.
[tex]h= \frac{3 * 264}{(6)^2\pi } =\frac{792}{113.04}=7[/tex] meters.
Therefore, the height of the cone is 7 meters.
