Final answer:
The formula for the radius of a cone based on its volume and height is r = √(³v / (πh)), which involves rearranging the given volume formula and solving for r.
Step-by-step explanation:
The question is asking for a formula to find the radius (r) of a cone based on its volume (v) and height (h). The formula for the volume of a cone is v = 1/3 πr²h. To solve for the radius, you can rearrange the formula as follows:
r = √(³v / (πh))
Here, you take the volume v, multiply by 3, then divide by the product of π and the height h. Finally, you take the square root of that entire expression to solve for the radius r.