The rate of change dV/dt of the volume V of a melting snowball is proportional to its surface area, so

for positive constant of proportionality k.
(a) Explain how the relationship between the surface area and volume of a sphere leads to the power 2/3.
(b) Suppose that you find a puddle of water that was formerly a snowball; that is, you now have V = 0. Can you tell when the snowball melted? Why?
(c) Solve the DE by separation of variables and draw several possible solution curves.
(d) How do your results fit with the Picard Theorem?

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