A water tank has the shape obtained by revolving the parabola around the y-axis. The water depth is 4 ft at 12 noon, when a circular plug in the bottom of the tank is removed. At 1 P.M. the depth of the water is 1 ft.

(a)Find the depth y(t) of water remaining after t hours.

(b)When will the tank be empty?

(c)If the initial radius of the top surface of the water is 2 ft, what is the radius of the circular hole in the bottom?

My working:

(a)

(b)

The tank will be empty at 1:08:34 P.M.

(c)

My textbook says that my answers for (a) and (b) are correct. But for (c), it has . Where have I gone wrong?