Math

QuestionSolve for hh in the cone volume formula: V=13πr2hV=\frac{1}{3} \pi r^{2} h.

Studdy Solution

STEP 1

Assumptions1. The formula for the volume of a cone is V=13πrhV=\frac{1}{3} \pi r^{} h . We are solving for hh

STEP 2

To isolate hh on one side of the equation, we first need to get rid of the fraction 1\frac{1}{} by multiplying both sides of the equation by.
V=1πr2hV = \cdot \frac{1}{} \pi r^{2} h

STEP 3

implify the right side of the equation.
3V=πr2h3V = \pi r^{2} h

STEP 4

Now, we need to isolate hh by dividing both sides of the equation by πr2\pi r^{2}.
3Vπr2=πr2hπr2\frac{3V}{\pi r^{2}} = \frac{\pi r^{2} h}{\pi r^{2}}

STEP 5

implify the equation to find the solution for hh.
h=3Vπr2h = \frac{3V}{\pi r^{2}}So, the height hh of the cone can be found using the formula h=3Vπr2h = \frac{3V}{\pi r^{2}}.

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