QPaperGen

Volume of a sphere: \(V = \frac{4}{3}\pi r^3\) \[\]

Differentiating:

\[\frac{dV}{dt} = \frac{d}{dr}\left(\frac{4}{3}\pi r^3\right) \cdot \frac{dr}{dt} = 4\pi r^2 \cdot \frac{dr}{dt}\]

Given \(\frac{dV}{dt} = 900\): This implies

\[900 = 4\pi (15)^2 \cdot \frac{dr}{dt} \Rightarrow \frac{dr}{dt} = \frac{900}{4\pi (225)} = \frac{1}{\pi} \text{cm/s}\]