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

To use Simpson's Rule, we need to divide the area into several sub-intervals with equal width. Looking at the intervals given in the table, we can see that the width is not constant, but we can still use Simpson's Rule by approximating the curve with a second-degree polynomial on each interval. We can then use the formula for Simpson's Rule with n=3, which gives:

Area ≈ ((b-a)/6) * [f(a) + 4f((a+b)/2) + f(b)] + ((c-b)/6) * [f(b) + 4f((b+c)/2) + f(c)]

Plugging in the values, we get:

Area ≈ ((200-0)/6) * [0 + 4(8000) + 10000] + ((400-200)/6) * [10000 + 4(12000) + 0] ≈ 106,666.67 sq ft

Therefore, the best choice is B.

Suppose a Land Developer Is Planning to Dig a Small