Please help me!

Question

A circular above-ground swimming pool has a 10-foot radius and may be filled to a maximum depth of 3 feet. If the depth of the water in the pool is rising at a rate of 0.4 inch per minute, at what rate is the water leaving the hose that is filling the pool? (Round your answer to one decimal place.)

 

_________gal/min

Answer 1

Let the volume of the pool V be π r² h where h is the height, h=h(t)

V= π r² h , Now differentiate using the chain rule
dV/dt is the water rate coming from the hose
dV/dt = (dV/dh).(dh/dt)
dh/dt is given as 0.4 in per min = 0.033 ft/min
dV/dt=(π r²). 0.033 = (3.14)(100). (0.033) = 10.36 ft³/min=(10.36).(7.48)=77.5 gal/min