Answer:
0.00318 ft/s
Explanation:
Volume of the inflatables swimming pool, V = πr²h
V = πr²h
a) (dh/dt) = (dh/dV) × (dV/dt)
V = πr²h
(dV/dh) = πr²
(dh/dV) = (1/πr²)
So, we require the rate of change of depth when diameter = 8 ft, radius = (diameter)/2 = 4 ft
(dh/dt) = (dh/dV) × (dV/dt)
(dh/dV) = (1/πr²) = (1/π(4²)) = 0.0199 ft⁻²
(dV/dt) = 0.12 gal/s = 0.016 ft³/s
(dh/dt) = (0.0199 × 0.016) = 0.00318 ft/s
