Answer:
dh/dt = 2/3*π ft/min
Step-by-step explanation:
We have a right circular cylinder, and water is pouring at a constant rate, we must expect the height of the water will rise a constant rate, therefore it does not matter the height
V(c) = π*r²*h ⇒ V(c) = π*(3)²*h ⇒ V(c) =9*π*h
DV(c)/dh = 9*π
DV(c)/dh = DV(c)/dt * dt/ dh ⇒ 9*π = DV(c)/dt * dt/ dh
dh/dt = DV(c)/dt / 9*π
DV(c)/dt = 6 ft³/m ( from problem statement )
Then
dh/dt = 6/9*π ft/min
dh/dt = 2/3*π ft/min
