Answer:
The height of the cone is [tex]h=9\ ft[/tex]
Step-by-step explanation:
we know that
The volume of a cone is equal to
[tex]V=\frac{1}{3}\pi r^{2}h[/tex]
In this problem we have
[tex]V=243\pi\ ft^{3}[/tex]
[tex]r=h\ ft[/tex]
substitute
[tex]243\pi=\frac{1}{3}\pi (h^{2})h[/tex]
simplify
[tex]729=(h^{3})[/tex]
[tex]h=\sqrt[3]{729}\ ft[/tex]
[tex]h=9\ ft[/tex]
