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Derive a formula for H from the formula for the volume of a cone P = (1/3)πr2H.

Mathematics

ScanSolve AI Answer

Answer

2Pπr2\frac{2P}{\pi r^2}

Step-by-step solution

3 steps

  1. Write down the given formula.

    P=12πr2HP = \frac{1}{2} \pi r^2 H

  2. Multiply both sides of the equation by 2 to eliminate the fraction.

    2P=πr2H2P = \pi r^2 H

  3. Divide both sides by πr2\pi r^2 to isolate HH.

    H=2Pπr2H = \frac{2P}{\pi r^2}

    The final answer is:

    H=2Pπr2H = \boxed{\frac{2P}{\pi r^2}}
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