Question

A spherical snowball is melting. Its radius is decreasing at 1.0 cm per hour when the radius is R cm. How fast is its volume decreasing at that time?

Answer 1

\[\frac{ dr }{ dt }=-1cm/hr\] when \(r=R\)

\(V=\frac{4}{3} \pi r^3 \rightarrow \frac{dV}{dt}=4 \pi r^2 \frac{dr}{dt}\)

\(\frac{dV}{dt}|r=R = 4 \pi (R)^2 (-1) = -4 \pi R^2 cm^3/hr \)

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