Snowball melting

Question

If a snowball melts so that its surface area decreases at a rate of 6 cm²/min, find the rate at which the diameter decreases when the diameter is 11 cm.

Answer 1

Given dS/dt = -6 cm²/min and S = 4π r² if we assume the snowball is spherical, then dS/dt = 8π r dr/dt = 8π (11/2) dr/dt = -6 from which dr/dt = -6 /44π = -0.0434 cm/min for the shrinkage rate of the radius. So the shrinkage rate of the diameter is twice as much, -0.087 cm/min.