Final answer:
The correct formula to express the height (h) in terms of the volume (V) for a cone is D. h = 3V / πr², which is obtained by rearranging the original volume formula V = 1/3 πr²h. Option number d is correct.
Step-by-step explanation:
The question is asking for the formula for the volume of a cone in terms of the height (h). The formula given is V = 1/3 πr²h. We need to rearrange this formula to solve for h.
Therefore, to find h in terms of V, you would isolate h on one side of the equation:
V = ⅓πr²h
× 3V = πr²h
h = 3V / (πr²)
Finally, the formula written in terms of h is h = 3V / (πr²), so the correct answer is D. h = 3V / πr².