QPaperGen

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

Differentiating with respect to \(r\):

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

When \(r = 10,\text{cm}\):

\[\frac{dV}{dr} = 4\pi (10)^2 = 400\pi \quad\text{cm}^3/\text{cm}\]