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Cloud moderators

13/12/2017 at 16:34

When a cone’s height is decreased by a factor of four, to maintain the same volume, the radius must be increased by a factor of two, or 100%. When the cone’s height is decreased by a factor of three, by what percent must the radius be increased to maintain the same volume? Express your answer to the nearest whole number.
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Phan Thanh Tinh Coordinator 15/01/2018 at 23:04

We have :

\(\dfrac{1}{3}\pi R^2h=\dfrac{1}{3}\pi.3R^2.\dfrac{1}{3}h=\dfrac{1}{3}\pi\left(\sqrt{3}R\right)^2.\dfrac{1}{3}h\)

So, the radius must be increased by \(\sqrt{3}\) times or :

\(\sqrt{3}.100-100\approx73\left(\%\right)\)

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