Question

the volume of a cone is 108π yd³, and its radius is 6 yd. what is the height of the cone, h?

Explanation:

Step1: Recall volume formula for cone

The volume formula of a cone is $V = \frac{1}{3}\pi r^{2}h$, where $V$ is volume, $r$ is radius and $h$ is height.

Step2: Substitute given values

We know $V = 108\pi$ and $r = 6$. Substituting into the formula gives $108\pi=\frac{1}{3}\pi(6)^{2}h$.

Step3: Simplify the equation

First, calculate $(6)^{2}=36$. The equation becomes $108\pi=\frac{1}{3}\pi\times36h$. Then, $\frac{1}{3}\times36 = 12$, so $108\pi = 12\pi h$.

Step4: Solve for $h$

Divide both sides of the equation $108\pi = 12\pi h$ by $12\pi$. $\frac{108\pi}{12\pi}=h$. Since $\frac{108}{12}=9$, we have $h = 9$.

Answer:

$9$