2. The trough shown in the figure to the right has dimensions as marked, in feet. Water is being withdrawn from the trough at a rate of 8 cubic feet per minute. At any time 1, let d be the depth and V be the volume of water in the trough.(Calculator permitted) a) Find the volume of water in the trough when it is full. b) Represent the volume as a function of the depth. c) What is the rate of change in d at the instant when the trough is 40% full? d) What is the rate of change in the area of the surface of the water (shaded in the figure) at the instant when the trough is 40% full.

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