14. (a) A cylindrical water tank has base area \(4 \mathrm {~m} ^ { 2 }\). The depth of the water at time \(t\) seconds is \(h\) metres. Water is poured in at the rate \(0.004 \mathrm {~m} ^ { 3 }\) per second. Water leaks from a hole in the bottom at a rate of \(0.0008 \mathrm { hm } ^ { 3 }\) per second. Show that $$5000 \frac { \mathrm {~d} h } { \mathrm {~d} t } \equiv 5 - h$$ [Hint: the volume, \(V\), of the cylindrical water tank is given by \(V = 4 h\).]
(b) Given that the tank is empty initially, find \(h\) in terms of \(t\).
(c) Find the depth of the water in the tank when \(t = 3600 \mathrm {~s}\), giving your answer correct to 2 decimal places.