Leaking Conical Tank A tank in the form of a rightcircular cone standing on end, ver...

Leaking Conical Tank A tank in the form of a rightcircular cone standing on end, vertex down, is leaking water through a circular hole in its bottom.

(a) Suppose the tank is 20 feet high and has radius 8 feet and the circular hole has radius 2 inches. In Problem 14 in Exercises 1.3 you were asked to show that the differential equation governing the height h of water leaking from a tank is

In this model, friction and contraction of the water at the hole were taken into account with c = 0.6, and g was taken to be 32 ft/s². See Figure 1.3.12. If the tank is initially full, how long will it take the tank to empty?

(b) Suppose the tank has a vertex angle of 60° and the circular hole has radius 2 inches. Determine the differential equation governing the height h of water. Use c = 0.6 and g = 32 ft/s². If the height of the water is initially 9 feet, how long will it take the tank to empty?

Reference: In Problem 14 in Exercises 1.3

The right-circular conical tank shown in Figure 1.3.12 loses water out of a circular hole at its bottom. Determine a differential equation for the height of the water h at time t. The radius of the hole is 2 in., g = 32 ft/s², and the friction/contraction factor introduced in Problem 13 is c = 0.6.