7. A swimming pool with a rectangular surface is 30 ft wide and 50 ft long. The volume of the pool is shaped as a prism (see drawing.) The table below shows the depth h(x) of the water at 5-ft intervals from one end of the pool to the other. a) 30 ft h(x) 0 5 Position (ft): x Depth (ft): h(x) 6.0 8.2 9.1 Data for the swimming pool 10 15 20 25 30 9.9 10.5 11.0 11.5 X Estimate the lateral area of the pool using a Riemann sum with the midpoints of five subintervals of equal length. b) Use this information to calculate the volume of water in the pool. (Hint: remember that the volume of a prism is the area of its base times the distance between the bases.) 50 ft 35 40 45 50 11.9 12.3 12.7 13.0