How rapidly is the radius of the disk increasing when the radius is 175 meters?

Question

A tank leaks  of oil into a lake. The oil forms a semicircular disk with a thickness of  meters. How rapidly is the radius of the disk increasing when the radius is  meters?The radius of the disk is increasing by  m/hr (round your answer to 3 decimal places)

Answer 1

Volume of half a cylinder, V=πr²h/2

dV/dt = 0.15 and h = 10^-6

dV/dt = πrhdr/dt --> dr/dt = (dV/dt)/(πrh)

When r = 175 meters:

dr/dt = (0.15)/(π(175)(10^-6) = 857.147/π ≈ 272.837 m/hr