(Draining a Hot Tub) Consider a cylindrical hot tub with a

Chapter 1, Problem 1.28

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(Draining a Hot Tub) Consider a cylindrical hot tub with a 5-foot radius and a height of 4 feet placed on one of its circular ends. Water is draining from the tub through a circular hole 5/8 inches in diameter in the base of the tub. (a) With k = 0.6, determine the rate at which the depth of the water is changing. Here it is useful to write dh dt = dh dV dV dt = dV/dt dV/dh . (b) Calculate the time T required to drain the hot tub if it is initially full. Hint: One way to do this is to write T = 0 H dt dh dh. (c) Determine how much longer it takes to drain the lower half than the upper half of the tub. Hint: Use the integral of part (b) with different limits for each half.