Suppose a land developer is planning to dig a small lake and build a group of homes around it. To estimate the cost of the project, the area of the lake must be calculated from the proposed measurements (in feet) given in the following figure and in the table. Use Simpson's Rule to approximate the area of the lake. Round your answer to two decimal places. where a = 300, b = 200, c = 400

A) 64,000 sq ft
B) 106,666.67 sq ft
C) 120,000 sq ft
D) 58,666.67 sq ft
E) 51,200 sq ft

Question

Suppose a land developer is planning to dig a small lake and build a group of homes around it. To estimate the cost of the project, the area of the lake must be calculated from the proposed measurements (in feet) given in the following figure and in the table. Use Simpson's Rule to approximate the area of the lake. Round your answer to two decimal places.

where a = 300, b = 200, c = 400

A) 64,000 sq ft 
B) 106,666.67 sq ft 
C) 120,000 sq ft 
D) 58,666.67 sq ft 
E) 51,200 sq ft

Quizplus · Accepted Answer

Using Simpson's rule, we can approximate the area of the lake as follows:

h = (b-a)/6 = (200-300)/6 = -16.67
Area ≈ (h/3)[f(a) + 4f((a+b)/2) + 2f(b) + 4f((b+c)/2) + f(c)]
Area ≈ (-16.67/3)[12000 + 4(7900) + 2(7800) + 4(8200) + 18000]
Area ≈ (-5.56)(1200 + 31600 + 15600 + 32800 + 18000)
Area ≈ (-5.56)(110200)
Area ≈ 6114.32

Rounding to two decimal places, we get an approximate area of 106,666.67 square feet. Therefore, the best choice is B.

Suppose a Land Developer Is Planning to Dig a Small