The problem asks to solve for $h$ in the formula for the volume of a cone:

$V = \frac{1}{3} B h$

Where:

• $V$ is the volume of the cone,
• $B$ is the area of the base (which is usually $B = \pi r^2$ for a circular base),
• $h$ is the height of the cone.

To solve for $h$:

1. Start with the given formula: $V = \frac{1}{3} B h$

2. Multiply both sides by 3 to eliminate the fraction: $3V = B h$

3. Finally, divide both sides by $B$ to isolate $h$: $h = \frac{3V}{B}$

So the height $h$ in terms of the volume $V$ and base area $B$ is: $h = \frac{3V}{B}$

Would you like further clarification or additional examples?

Related questions:

1. How do you calculate the base area $B$ of a cone with a circular base?
2. What happens to the height if the volume of the cone is doubled?
3. How can you calculate the volume of a cone given the radius and height?
4. If you know the slant height of a cone, how can you find its vertical height?
5. How does changing the radius affect the volume of the cone?

Tip:

Remember that for cones with circular bases, the base area $B = \pi r^2$, where $r$ is the radius of the base.