The formula given for the volume of a cone is:

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

You are asked to solve for $h$ (the height of the cone).

Step 1: Multiply both sides of the formula by 3

We multiply both sides by 3 to eliminate the fraction:

$3V = \pi r^2 h$

Step 2: Divide both sides by $\pi r^2$

Now, to isolate $h$, divide both sides by $\pi r^2$:

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

Thus, the solution for $h$ is:

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

Would you like further details or explanations?

Here are 5 related questions to deepen understanding:

1. What is the formula for the surface area of a cone?
2. How would you solve for the radius $r$ in the same volume formula?
3. How does the volume of a cone compare to the volume of a cylinder with the same base and height?
4. If the volume and radius are known, how can you find the height?
5. How does changing the height affect the volume of the cone?

Tip:

When solving equations with fractions, multiplying both sides by the denominator helps eliminate the fraction and simplify your work.