Answer
$\frac{3}{80\pi}\,in/min$
Work Step by Step
$\frac{dV}{dt}= 15\,\frac{ in^{3}}{min}$ (given)
$15= \frac{d}{dt}(\frac{4}{3}\pi r^{3})=$
$\frac{d}{dr}(\frac{4}{3}\pi r^{3})\times\frac{dr}{dt}=4\pi r^{2}\times\frac{dr}{dt}$
$\implies \frac{15}{4\pi r^{2}}=\frac{dr}{dt}$
When r= 10 in, we have
$\frac{dr}{dt}=\frac{15}{4\pi\times10^{2}}=\frac{3}{80\pi}\,in/min$
