Replace $V$ with $120\pi$ and $r$ with $6$ in the formula. What equation in terms of $h$ do you get?

After simplifying $r^2$ and $\tfrac13 \cdot r^2$, you will have a simple one-step equation in $h$. Divide both sides by the coefficient of $h$ to solve.

Type y = (1/3)*pi*36*x into Desmos, where $x$ represents the height $h$ and $36 = 6^2$ is the squared radius.

On a new line, type y = 120*pi. Click on the intersection point. The x-coordinate is the height of the cone.

The formula for the volume of a right circular cone is

You are told the volume is $120\pi$ and the radius is $6$, so substitute $V=120\pi$ and $r=6$:

First compute $6^2$:

So the equation becomes

Now simplify $\tfrac{1}{3}\cdot 36$:

So the equation is

To solve for $h$, divide both sides of

by $12\pi$:

The $\pi$ cancels, and $120 \div 12 = 10$, so

Therefore, the height of the cone is $10$ centimeters.