Leaking Cylindrical Tank A tank in the form of a right circular cylinder standing on...

Leaking Cylindrical Tank A tank in the form of a right circular cylinder standing on end is leaking water through a circular hole in its bottom. As we saw in (10) of Section 1.3, when friction and contraction of water at the hole are ignored, the height h of water in the tank is described by

where are the cross-sectional areas of the water and the hole, respectively.

(a) Solve for h(t) if the initial height of the water is H. By hand, sketch the graph of h(t) and give its interval I of definition in terms of the symbols Use

(b) Suppose the tank is 10 ft high and has radius 2 ft and the circular hole has radius in. If the tank is initially full, how long will it take to empty?