The formula for volume of a sphere is
\(V=\frac{4}{3}\pi r^{3}\)
\(\rightarrow\frac{dV}{dt}=4\pi r^{2}\frac{dr}{dt}\)
If the diameter is 1.3, then \(r=\frac{1.3}{2}=0.65\)
We are given
\(\frac{dV}{dt}=2.7\) and \(r=0.65\)
\(\rightarrow2.7=4\pi(0.65)^{2}\frac{dr}{dt}\)
\(\rightarrow\frac{dr}{dt}=\frac{2.7}{4\pi(0.65)^{2}}\approx0.5085\ ft/min\)
Change in diameter is twice change in radius, so we get 2*0.5085=1.017 ft/min
