The question wants us to find 3 times the volume of the pool. This is because we are told that the pool must be filled 3 times during the summer and asked how many cubic feet of water is required to fill the pool all summer.
Step 1: Find the volume of the pool. Volume is calculated by multiplying length by width by height. Pool length = 5 ft. Pool width = 4 ft. Pool height = 2 ft. Pool volume = 5 • 4 • 2 5 • 4 • 2 = 40 The volume of the pool is 40 cubic feet.
Step 2: Find 3 times the volume of the pool. Volume = 40 ft.^3 3 times volume = 3 • 40 ft.^3 3 • 40 ft.^3 = 120 ft.^3 3 times the volume of the pool is 120 cubic feet.
Answer: The pool requires 120 cubic feet of water in order to be filled enough over the course of the summer.
The two curves intersect at two points, (0, 0) and (8, 8):
The area of a semicircle with diameter is . The diameter of each cross-section is determined by the vertical distance between the two curves for any given value of between 0 and 8. Over this interval, and , so the volume of this solid is given by the integral
