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

Using Simpson's rule, we can approximate the surface area by dividing the lake into 10 sections, each with a width of 20 ft. Then, we can calculate the area of each section using the trapezoidal rule (since Simpson's rule requires an even number of sections).

Using this method, we get the following areas for each section:

Section 1: 1/2 (70 + 60)(20) = 1300
Section 2: 1/2 (60 + 50)(20) = 1100
Section 3: 1/2 (50 + 45)(20) = 950
Section 4: 1/2 (45 + 50)(20) = 950
Section 5: 1/2 (50 + 60)(20) = 1100
Section 6: 1/2 (60 + 70)(20) = 1300
Section 7: 1/2 (70 + 75)(20) = 1450
Section 8: 1/2 (75 + 75)(20) = 1500
Section 9: 1/2 (75 + 70)(20) = 1450
Section 10: 1/2 (70 + 60)(20) = 1300

The total surface area is the sum of these areas, or:

1300 + 1100 + 950 + 950 + 1100 + 1300 + 1450 + 1500 + 1450 + 1300 = 12600

Rounding to the nearest tenth, we get:

Answer: C) 12600.0.

A Manmade Lake Located in Lake View Condominiums Has the Shape