() A large container made to hold water has the equation z = 4(x + y) 3/2 (The z-axis points up.) (a) Find a formula for V(z), the volume of water in the container when its depth is z. ANSWER: V(z) = (b) Suppose that the container is filled to a depth H > 0. At a certain instant, a hole develops at the origin and water starts to drain out. This makes the water depth z a decreasing function of time; the water depth has dropped to H/2 exactly 60 minutes after draining begins. Find the first time when all the water is gone; call this T. ANSWER: T = Background: According to Bernoulli's Law, the instantaneous rate of volume loss from a container like ours is proportional to the square root of the water depth.