A spherical balloon is inflated so that its volume is increasing at the rate of 7 ft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 5 feet?

Question

A spherical balloon is inflated so that its volume is increasing at the rate of 7 ft3/min. How rapidly is the diameter of the balloon increasing when the diameter is 5 feet?

Answer 1

given: dVolume/dt = 7 f³/min find: dDiameter/dt ... note: volume of a sphere = πD³/6 = V find dV/dt=πD²/3* dD/dt (don't forget chain rule). Rearrange to find dD/dt = dV/dt *(2/πD²). Substitute given values for dV/dt and D finding dD/dt=.178 feet/min.