Consider an initially full hemispherical water tank of radius 4 ft, where the radius r of its circular bottom hole is now unknown. At 1 P.M. the bottom hole is opened and at 1:30 P.M. the depth of water in the tank is 2ft.

(a) Use Torricelli's law in the form (taking constriction into account) to determine when the tank will be empty.

(b) What is the radius of the bottom hole?

My working: