In standard calculus textbooks—usually as a problem on related rates—it is shown that for a snowball melting at a rate proportional to its surface area, its radius decreases at a constant rate regardless of its initial size. A further assumption (usually unstated) is that the snowball remains spherical as it melts.

Question 1:

Question 2: Show that the same volume reduction factor applies for cubes of side L(t) and pL(t).

(Assume that the cubes are suspended from a corner so that all faces are exposed to warm air.)

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