Question

The formula for the volume, V, of a cone having the radius, r, and the height, h, is shown below:

V = (1/3) * π * r^2 * h

What is the formula to calculate the height, h, of the cone?

A) h = V / (1/3 * π * r^2)
B) h = V * 3 / (π * r^2)
C) h = V / (π * r^2)
D) h = V / (3 * π * r^2)

Answer 1

The formula to calculate the height of the cone given its volume V and radius r is h = V * 3 / (π * r^2), corresponding to option B.

Step-by-step explanation:

To find the formula to calculate the height, h, of a cone when given its volume, V, and radius, r, we start by rearranging the original formula for volume, V = (1/3) * π * r^2 * h. To solve for h, we need to isolate it on one side of the equation:

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• Multiply both sides of the equation by 3 to get rid of the fraction: 3V = π * r^2 * h.
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• Divide both sides of the new equation by π * r^2 to isolate h: h = (3V) / (π * r^2).

Therefore, the formula to calculate the height of the cone is h = V * 3 / (π * r^2), which corresponds to option B.