Question

The equation above can be used to calculate the volume V, of a cone with a height h and radius r. If the volume of a cone is 243?ft3, and the height is equal to the radius of the base, what is the height of the cone in feet?

Answer 1

Answer:

The height of the cone is $h=9\ ft$

Step-by-step explanation:

we know that

The volume of a cone is equal to

$V=\frac{1}{3}\pi r^{2}h$

In this problem we have

$V=243\pi\ ft^{3}$

$r=h\ ft$

substitute

$243\pi=\frac{1}{3}\pi (h^{2})h$

simplify

$729=(h^{3})$

$h=\sqrt[3]{729}\ ft$

$h=9\ ft$