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Calculate the volume of the earthwork (in cubic meter) using trapezoidal method if the cross section areas of the three section of embankment at an interval of 20 m are 40 square meters, 50 square meters and 80 square meters.
- a)1067
- b)1700
- c)2200
- d)3200
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Calculate the volume of the earthwork (in cubic meter) using trapezoid...
h(internal) = 20 m
A1 = 40 m2
A2 = 50 m2
A3 = 80 m3
Using trapezoidal formula
Volumeofearthwork=h 
V = 2200 m3
Most Upvoted Answer
Calculate the volume of the earthwork (in cubic meter) using trapezoid...
To calculate the volume of earthwork using the trapezoidal method, we need to find the average areas of the cross sections and then multiply them by the distance between the cross sections.
Step 1: Calculate the average areas of adjacent cross sections
- The three cross section areas given are 40 m², 50 m², and 80 m².
- To find the average area between the first and second cross sections, add the two areas and divide by 2: (40 + 50) / 2 = 45 m².
- To find the average area between the second and third cross sections, add the two areas and divide by 2: (50 + 80) / 2 = 65 m².
Step 2: Calculate the distance between cross sections
- The distance between each cross section is given as 20 m.
Step 3: Calculate the volume of each trapezoid
- The volume of a trapezoid can be calculated using the formula: Volume = (Average Area1 + Average Area2) * Distance / 2.
- For the first trapezoid: Volume1 = (40 + 45) * 20 / 2 = 850 m³.
- For the second trapezoid: Volume2 = (45 + 65) * 20 / 2 = 1100 m³.
Step 4: Calculate the total volume
- Add the volumes of all the trapezoids: Total Volume = Volume1 + Volume2 = 850 + 1100 = 1950 m³.
Therefore, the volume of the earthwork using the trapezoidal method is 1950 cubic meters. None of the given options match the calculated volume, so the correct answer cannot be determined from the options provided.
Step 1: Calculate the average areas of adjacent cross sections
- The three cross section areas given are 40 m², 50 m², and 80 m².
- To find the average area between the first and second cross sections, add the two areas and divide by 2: (40 + 50) / 2 = 45 m².
- To find the average area between the second and third cross sections, add the two areas and divide by 2: (50 + 80) / 2 = 65 m².
Step 2: Calculate the distance between cross sections
- The distance between each cross section is given as 20 m.
Step 3: Calculate the volume of each trapezoid
- The volume of a trapezoid can be calculated using the formula: Volume = (Average Area1 + Average Area2) * Distance / 2.
- For the first trapezoid: Volume1 = (40 + 45) * 20 / 2 = 850 m³.
- For the second trapezoid: Volume2 = (45 + 65) * 20 / 2 = 1100 m³.
Step 4: Calculate the total volume
- Add the volumes of all the trapezoids: Total Volume = Volume1 + Volume2 = 850 + 1100 = 1950 m³.
Therefore, the volume of the earthwork using the trapezoidal method is 1950 cubic meters. None of the given options match the calculated volume, so the correct answer cannot be determined from the options provided.
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Calculate the volume of the earthwork (in cubic meter) using trapezoidal method if the cross section areas of the three section of embankment at an interval of 20 m are 40 square meters, 50 square meters and 80 square meters.a)1067b)1700c)2200d)3200Correct answer is option 'C'. Can you explain this answer?
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Calculate the volume of the earthwork (in cubic meter) using trapezoidal method if the cross section areas of the three section of embankment at an interval of 20 m are 40 square meters, 50 square meters and 80 square meters.a)1067b)1700c)2200d)3200Correct answer is option 'C'. 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 volume of the earthwork (in cubic meter) using trapezoidal method if the cross section areas of the three section of embankment at an interval of 20 m are 40 square meters, 50 square meters and 80 square meters.a)1067b)1700c)2200d)3200Correct answer is option 'C'. 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 volume of the earthwork (in cubic meter) using trapezoidal method if the cross section areas of the three section of embankment at an interval of 20 m are 40 square meters, 50 square meters and 80 square meters.a)1067b)1700c)2200d)3200Correct answer is option 'C'. Can you explain this answer?.
Calculate the volume of the earthwork (in cubic meter) using trapezoidal method if the cross section areas of the three section of embankment at an interval of 20 m are 40 square meters, 50 square meters and 80 square meters.a)1067b)1700c)2200d)3200Correct answer is option 'C'. 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 volume of the earthwork (in cubic meter) using trapezoidal method if the cross section areas of the three section of embankment at an interval of 20 m are 40 square meters, 50 square meters and 80 square meters.a)1067b)1700c)2200d)3200Correct answer is option 'C'. 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 volume of the earthwork (in cubic meter) using trapezoidal method if the cross section areas of the three section of embankment at an interval of 20 m are 40 square meters, 50 square meters and 80 square meters.a)1067b)1700c)2200d)3200Correct answer is option 'C'. Can you explain this answer?.
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