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28Tylerr
Is it possible for a sphere to have the same numerical value for the surface area and volume? Find the radius of a sphere.
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.
We also have the degenerate case of r=0, but that's pretty uninteresting.