A pond is approximately circular, with a diameter of 400 feet. Starting at the center, the depth of the water is measured every 25 feet and recorded in the table (see figure).

(a) Use Simpson’s Rule to approximate the volume of water in the pond.
(b) Use the regression capabilities of a graphing utility to find a quadratic model for the depths recorded in the table. Use the graphing utility to plot the depths and graph the model.
(c) Use the integration capabilities of a graphing utility and the model in part (b) to approximate the volume of water in the pond.
(d) Use the result of part (c) to approximate the number of gallons of water in the pond.

Transcribed Image Text:

0 25 50 Depth 20 19 19 X X Depth X 75 100 125 17 15 14 150 175 200 Depth 10 6 0 Depth y 20 18. 16 14 12. 10 208642 2- 50 100 150 200 Distance from center X