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anonymous 3 years ago Is it possible for a sphere to have the same numerical value for the surface area and volume? Find the radius of a sphere.

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1. anonymous

Since the surface area is $A = 4\pi*r^2$ and the volume is $V = \frac{4}{3}\pi*r^3,$ and want these quantities to be equal we get $4\pi*r^2 = \frac{4}{3}\pi*r^3.$ We cancel 4πr^2 from both sides and get $1 = \frac{1}{3}*r$ which means that r=3.

2. anonymous

We also have the degenerate case of r=0, but that's pretty uninteresting.

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