A manmade lake located in Lake View Condominiums has the shape depicted in the following figure. The measurements shown were taken at 10-ft intervals. Using Simpson's rule with , estimate the surface area of the lake. Round the result to the nearest tenth.

Question

A manmade lake located in Lake View Condominiums has the shape depicted in the following figure. The measurements shown were taken at 10-ft intervals. Using Simpson's rule with  , estimate the surface area of the lake. Round the result to the nearest tenth.

Quizplus · Accepted Answer

To use Simpson's rule, we need an odd number of intervals. Since we have measurements every 10 feet, we have a total of 6 intervals between 0 and 50. Adding an extra midpoint measurement at 25 feet gives us a total of 7 measurements and 6 intervals. Applying Simpson's rule, we get:

Surface Area = (10/3)[20 + 4(24) + 2(38) + 4(32) + 2(41) + 4(36) + 20]

Surface Area ≈ 883.3 square feet, rounded to the nearest tenth.

Therefore, the best choice is C.

A Manmade Lake Located in Lake View Condominiums Has the Shape