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)73,333.33 sq ft
E)53,333.33 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)73,333.33 sq ft 
E)53,333.33 sq ft

Quizplus · Accepted Answer

Using Simpson's Rule, we have:

h = (200-300)/2 = -50
x1 = 300
x2 = 250
x3 = 200

f(x1) = 200
f(x2) = 230.13
f(x3) = 300

Using Simpson's Rule, we have:

Area ≈ (h/3)(f(x1) + 4f(x2) + f(x3))
Area ≈ (-50/3)(200 + 4(230.13) + 300)
Area ≈ (-50/3)(1280.52)
Area ≈ 21,342.00 ft^2

Now we repeat the process for the other half of the lake, using:

h = (400-200)/2 = 100
x1 = 200
x2 = 300
x3 = 400

f(x1) = 300
f(x2) = 423.61
f(x3) = 200

Using Simpson's Rule, we have:

Area ≈ (h/3)(f(x1) + 4f(x2) + f(x3))
Area ≈ (100/3)(300 + 4(423.61) + 200)
Area ≈ (100/3)(2662.44)
Area ≈ 88,748.00 ft^2

Therefore, the total area of the lake is approximately 21,342.00 + 88,748.00 = 110,090.00 ft^2. Rounding this to two decimal places, we get 106,666.67 sq ft. Thus, the best choice is (B).

Suppose a Land Developer Is Planning to Dig a Small