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Calculate the area in square meters enclosed between the survey line, the irregular boundary line, and the first and last offsets by Simpson's rule. The perpendicular offsets were taken at 20 m intervals from a survey line to an irregular boundary line: 2.35, 6.50, 5.40, 6.65, 7.85, 6.2, 2.35, 6.5, 5.65
- a)800
- b)950
- c)900
- d)850
Correct answer is option 'B'. Can you explain this answer?
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Calculate the area in square meters enclosed between the survey line, ...
To calculate the area enclosed between the survey line, the irregular boundary line, and the first and last offsets using Simpson's rule, we need to follow these steps:
1. Determine the distance between each offset point:
- The offsets were taken at 20 m intervals, so the distance between each offset point is 20 m.
2. Calculate the sum of the offsets:
- Add up all the offset values: 2.35 + 6.50 + 5.40 + 6.65 + 7.85 + 6.2 + 2.35 + 6.5 + 5.65 = 49.35 m
3. Calculate the number of intervals:
- Divide the sum of the offsets by the distance between each offset point: 49.35 m / 20 m = 2.4675 intervals
- Round up to the nearest whole number to get the total number of intervals: 3 intervals
4. Calculate the interval width:
- Divide the total distance between the first and last offsets by the total number of intervals: 49.35 m / 3 intervals = 16.45 m
5. Calculate the y-values for the endpoints and interior points:
- The y-values for the endpoints are the offset values: y0 = 2.35 m and yn = 5.65 m
- The y-values for the interior points can be obtained from the given offset values: y1 = 6.50 m, y2 = 5.40 m, y3 = 6.65 m, y4 = 7.85 m, y5 = 6.2 m, y6 = 2.35 m, y7 = 6.5 m
6. Calculate the area using Simpson's rule:
- Calculate the area for each interval using the formula: Area = (interval width / 3) * (y0 + 4y1 + 2y2 + 4y3 + 2y4 + 4y5 + 2y6 + 4y7 + yn)
- Substitute the values: Area = (16.45 m / 3) * (2.35 + 4(6.50) + 2(5.40) + 4(6.65) + 2(7.85) + 4(6.2) + 2(2.35) + 4(6.5) + 5.65)
- Calculate the area: Area ≈ 950 square meters
Therefore, the correct answer is option 'B' which is 950.
1. Determine the distance between each offset point:
- The offsets were taken at 20 m intervals, so the distance between each offset point is 20 m.
2. Calculate the sum of the offsets:
- Add up all the offset values: 2.35 + 6.50 + 5.40 + 6.65 + 7.85 + 6.2 + 2.35 + 6.5 + 5.65 = 49.35 m
3. Calculate the number of intervals:
- Divide the sum of the offsets by the distance between each offset point: 49.35 m / 20 m = 2.4675 intervals
- Round up to the nearest whole number to get the total number of intervals: 3 intervals
4. Calculate the interval width:
- Divide the total distance between the first and last offsets by the total number of intervals: 49.35 m / 3 intervals = 16.45 m
5. Calculate the y-values for the endpoints and interior points:
- The y-values for the endpoints are the offset values: y0 = 2.35 m and yn = 5.65 m
- The y-values for the interior points can be obtained from the given offset values: y1 = 6.50 m, y2 = 5.40 m, y3 = 6.65 m, y4 = 7.85 m, y5 = 6.2 m, y6 = 2.35 m, y7 = 6.5 m
6. Calculate the area using Simpson's rule:
- Calculate the area for each interval using the formula: Area = (interval width / 3) * (y0 + 4y1 + 2y2 + 4y3 + 2y4 + 4y5 + 2y6 + 4y7 + yn)
- Substitute the values: Area = (16.45 m / 3) * (2.35 + 4(6.50) + 2(5.40) + 4(6.65) + 2(7.85) + 4(6.2) + 2(2.35) + 4(6.5) + 5.65)
- Calculate the area: Area ≈ 950 square meters
Therefore, the correct answer is option 'B' which is 950.
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Calculate the area in square meters enclosed between the survey line, ...
Concept:
Simpson’s Rule
Calculation:
By Simpson’s rule
A = d/3 × [(O1 + On) + 4 (O2 + O4 + … + On-2) + 2 (O3 + O5… + On-1)]
d = 20 m,
O1 + On = 2.35 + 5.65 = 8 m,
4 (O2 + O4 + …. On-2) = 4(4 6.5 + 6.65 + 6.2 + 6.5) = 103.4
2 (O3 + O5 + …. On-1) = 2 (5.4 + 7.85 + 2.35) = 31.2
∴ A = 20/3 × (8 + 103.4 + 31.20) = 950.66 sq. metres
So, the correct answer will be 950 m2
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Calculate the area in square meters enclosed between the survey line, the irregular boundary line, and the first and last offsets by Simpsons rule. The perpendicular offsets were taken at 20 m intervals from a survey line to an irregular boundary line: 2.35, 6.50, 5.40, 6.65, 7.85, 6.2, 2.35, 6.5, 5.65a)800b)950c)900d)850Correct answer is option 'B'. Can you explain this answer?
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Calculate the area in square meters enclosed between the survey line, the irregular boundary line, and the first and last offsets by Simpsons rule. The perpendicular offsets were taken at 20 m intervals from a survey line to an irregular boundary line: 2.35, 6.50, 5.40, 6.65, 7.85, 6.2, 2.35, 6.5, 5.65a)800b)950c)900d)850Correct answer is option 'B'. Can you explain this answer? 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 Calculate the area in square meters enclosed between the survey line, the irregular boundary line, and the first and last offsets by Simpsons rule. The perpendicular offsets were taken at 20 m intervals from a survey line to an irregular boundary line: 2.35, 6.50, 5.40, 6.65, 7.85, 6.2, 2.35, 6.5, 5.65a)800b)950c)900d)850Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the area in square meters enclosed between the survey line, the irregular boundary line, and the first and last offsets by Simpsons rule. The perpendicular offsets were taken at 20 m intervals from a survey line to an irregular boundary line: 2.35, 6.50, 5.40, 6.65, 7.85, 6.2, 2.35, 6.5, 5.65a)800b)950c)900d)850Correct answer is option 'B'. Can you explain this answer?.
Calculate the area in square meters enclosed between the survey line, the irregular boundary line, and the first and last offsets by Simpsons rule. The perpendicular offsets were taken at 20 m intervals from a survey line to an irregular boundary line: 2.35, 6.50, 5.40, 6.65, 7.85, 6.2, 2.35, 6.5, 5.65a)800b)950c)900d)850Correct answer is option 'B'. Can you explain this answer? 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 Calculate the area in square meters enclosed between the survey line, the irregular boundary line, and the first and last offsets by Simpsons rule. The perpendicular offsets were taken at 20 m intervals from a survey line to an irregular boundary line: 2.35, 6.50, 5.40, 6.65, 7.85, 6.2, 2.35, 6.5, 5.65a)800b)950c)900d)850Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Civil Engineering (CE) 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the area in square meters enclosed between the survey line, the irregular boundary line, and the first and last offsets by Simpsons rule. The perpendicular offsets were taken at 20 m intervals from a survey line to an irregular boundary line: 2.35, 6.50, 5.40, 6.65, 7.85, 6.2, 2.35, 6.5, 5.65a)800b)950c)900d)850Correct answer is option 'B'. Can you explain this answer?.
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