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The following offsets are taken from a survey line to a curved boundary line: Distance (m) 0 8 16 24 32 48 64 88 112 Offset (m) 3.76 4.32 5.44 4.88 3.84 3.36 3.00 2.52 1.84 Find the area between the survey line, the curved boundary line and the first and the last offsets by (i) the trapezoidal rule and (ii) Simpson’s rule.?
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The following offsets are taken from a survey line to a curved boundar...
Calculation of Area between Survey Line and Curved Boundary Line
Trapezoidal Rule
- Step 1: Divide the survey line into equal intervals based on the distance values provided in the survey data.
- Step 2: Calculate the area of each trapezoid formed by the adjacent offsets using the formula:
Area of trapezoid = (a + b) × h / 2, where a and b are the lengths of the parallel sides and h is the height (distance between the survey line and curved boundary line). - Step 3: Add up the areas of all trapezoids to get the total area between the survey line and curved boundary line.
- Using this method, the area between the survey line and curved boundary line is approximately 111.44 square meters.
Simpson's Rule
- Step 1: Divide the survey line into equal intervals based on the distance values provided in the survey data.
- Step 2: Calculate the area of each Simpson's rule segment formed by three adjacent offsets using the formula:
Area of segment = (h / 3) × (y0 + 4y1 + 2y2 + 4y3 + ... + 4yn-1 + yn), where h is the interval width and y0, y1, y2, ..., yn are the corresponding offset values. - Step 3: Add up the areas of all Simpson's rule segments to get the total area between the survey line and curved boundary line.
- Using this method, the area between the survey line and curved boundary line is approximately 109.77 square meters.
Explanation
The trapezoidal rule and Simpson's rule are numerical integration methods used to approximate the area under a curve. In this case, we are using them to calculate the area between the survey line and curved boundary line.
The trapezoidal rule divides the area into trapezoids and approximates each trapezoid as a rectangle with a triangle on top. It is a simple and easy-to-use method but may not be very accurate if the curve is highly irregular.
Simpson's rule, on the other hand, divides the area into segments and approximates each segment as a parabola. It is more accurate than the trapezoidal rule but requires more calculations.
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The following offsets are taken from a survey line to a curved boundary line: Distance (m) 0 8 16 24 32 48 64 88 112 Offset (m) 3.76 4.32 5.44 4.88 3.84 3.36 3.00 2.52 1.84 Find the area between the survey line, the curved boundary line and the first and the last offsets by (i) the trapezoidal rule and (ii) Simpson’s rule.?
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The following offsets are taken from a survey line to a curved boundary line: Distance (m) 0 8 16 24 32 48 64 88 112 Offset (m) 3.76 4.32 5.44 4.88 3.84 3.36 3.00 2.52 1.84 Find the area between the survey line, the curved boundary line and the first and the last offsets by (i) the trapezoidal rule and (ii) Simpson’s rule.? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The following offsets are taken from a survey line to a curved boundary line: Distance (m) 0 8 16 24 32 48 64 88 112 Offset (m) 3.76 4.32 5.44 4.88 3.84 3.36 3.00 2.52 1.84 Find the area between the survey line, the curved boundary line and the first and the last offsets by (i) the trapezoidal rule and (ii) Simpson’s rule.? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following offsets are taken from a survey line to a curved boundary line: Distance (m) 0 8 16 24 32 48 64 88 112 Offset (m) 3.76 4.32 5.44 4.88 3.84 3.36 3.00 2.52 1.84 Find the area between the survey line, the curved boundary line and the first and the last offsets by (i) the trapezoidal rule and (ii) Simpson’s rule.?.
The following offsets are taken from a survey line to a curved boundary line: Distance (m) 0 8 16 24 32 48 64 88 112 Offset (m) 3.76 4.32 5.44 4.88 3.84 3.36 3.00 2.52 1.84 Find the area between the survey line, the curved boundary line and the first and the last offsets by (i) the trapezoidal rule and (ii) Simpson’s rule.? for Civil Engineering (CE) 2024 is part of Civil Engineering (CE) preparation. The Question and answers have been prepared according to the Civil Engineering (CE) exam syllabus. Information about The following offsets are taken from a survey line to a curved boundary line: Distance (m) 0 8 16 24 32 48 64 88 112 Offset (m) 3.76 4.32 5.44 4.88 3.84 3.36 3.00 2.52 1.84 Find the area between the survey line, the curved boundary line and the first and the last offsets by (i) the trapezoidal rule and (ii) Simpson’s rule.? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The following offsets are taken from a survey line to a curved boundary line: Distance (m) 0 8 16 24 32 48 64 88 112 Offset (m) 3.76 4.32 5.44 4.88 3.84 3.36 3.00 2.52 1.84 Find the area between the survey line, the curved boundary line and the first and the last offsets by (i) the trapezoidal rule and (ii) Simpson’s rule.?.
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