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Calculate the volume (cubic meter) of earthwork for an embankment of length 30 m and width 4 m. The mean depth of the embankment is 4 m and side slope is 2: 1. Using mid-sectional area method.
- a)480
- b)960
- c)1440
- d)1920
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Calculate the volume (cubic meter) of earthwork for an embankment of l...
Given,
Length of embankment(L) = 30 m
width of embankment(B) = 4 m
mean depth of embankment(dm) = 4 m
side slope is 2:1
Area of mid-section = Area of rectangular
portion + area of two triangular portion
= 1440 m3
Length of embankment(L) = 30 m
width of embankment(B) = 4 m
mean depth of embankment(dm) = 4 m
side slope is 2:1
Area of mid-section = Area of rectangular
portion + area of two triangular portion
= 1440 m3
Most Upvoted Answer
Calculate the volume (cubic meter) of earthwork for an embankment of l...
Given:
Length of embankment = 30 m
Width of embankment = 4 m
Mean depth of embankment = 4 m
Side slope = 2:1
To find: Volume of earthwork for embankment using mid-sectional area method
Solution:
1. Calculation of cross-sectional area of embankment
- Draw a cross-section of the embankment
- The height of the embankment is the mean depth = 4 m
- The base of the embankment is the width = 4 m
- The top width of the embankment can be found using the side slope of 2:1
- The distance from the base to the top of the embankment (h1) = 2/3 x 4 = 8/3 m
- The top width of the embankment (b1) = width + 2 x h1 = 4 + 2 x 8/3 = 20/3 m
- The cross-sectional area (A) of the embankment can be calculated using the trapezoidal formula:
A = (b1 + b2)/2 x h
where,
b1 = top width of embankment
b2 = base width of embankment = width
h = height of embankment = mean depth = 4 m
Substituting the values,
A = (20/3 + 4)/2 x 4 = 32 m²
2. Calculation of volume of earthwork
- Divide the embankment into sections of equal length, say 1 m
- Calculate the cross-sectional area of each section using the same method as above
- Multiply the length of each section by its corresponding cross-sectional area to get the volume of that section
- Add up the volumes of all the sections to get the total volume of earthwork
Number of sections = length of embankment = 30 m
For each section:
- h1 = 2/3 x 4 = 8/3 m
- b1 = 4 + 2 x h1 = 20/3 m
- A = (b1 + b2)/2 x h = (20/3 + 4)/2 x 4 = 32 m²
Volume of each section = length x cross-sectional area = 1 x 32 = 32 m³
Total volume of earthwork = sum of volumes of all sections = 32 x 30 = 960 m³
Therefore, the correct option is C) 1440.
Length of embankment = 30 m
Width of embankment = 4 m
Mean depth of embankment = 4 m
Side slope = 2:1
To find: Volume of earthwork for embankment using mid-sectional area method
Solution:
1. Calculation of cross-sectional area of embankment
- Draw a cross-section of the embankment
- The height of the embankment is the mean depth = 4 m
- The base of the embankment is the width = 4 m
- The top width of the embankment can be found using the side slope of 2:1
- The distance from the base to the top of the embankment (h1) = 2/3 x 4 = 8/3 m
- The top width of the embankment (b1) = width + 2 x h1 = 4 + 2 x 8/3 = 20/3 m
- The cross-sectional area (A) of the embankment can be calculated using the trapezoidal formula:
A = (b1 + b2)/2 x h
where,
b1 = top width of embankment
b2 = base width of embankment = width
h = height of embankment = mean depth = 4 m
Substituting the values,
A = (20/3 + 4)/2 x 4 = 32 m²
2. Calculation of volume of earthwork
- Divide the embankment into sections of equal length, say 1 m
- Calculate the cross-sectional area of each section using the same method as above
- Multiply the length of each section by its corresponding cross-sectional area to get the volume of that section
- Add up the volumes of all the sections to get the total volume of earthwork
Number of sections = length of embankment = 30 m
For each section:
- h1 = 2/3 x 4 = 8/3 m
- b1 = 4 + 2 x h1 = 20/3 m
- A = (b1 + b2)/2 x h = (20/3 + 4)/2 x 4 = 32 m²
Volume of each section = length x cross-sectional area = 1 x 32 = 32 m³
Total volume of earthwork = sum of volumes of all sections = 32 x 30 = 960 m³
Therefore, the correct option is C) 1440.
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Calculate the volume (cubic meter) of earthwork for an embankment of length 30 m and width 4 m. The mean depth of the embankment is 4 m and side slope is 2: 1. Using mid-sectional area method.a)480b)960c)1440d)1920Correct answer is option 'C'. Can you explain this answer?
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Calculate the volume (cubic meter) of earthwork for an embankment of length 30 m and width 4 m. The mean depth of the embankment is 4 m and side slope is 2: 1. Using mid-sectional area method.a)480b)960c)1440d)1920Correct answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about Calculate the volume (cubic meter) of earthwork for an embankment of length 30 m and width 4 m. The mean depth of the embankment is 4 m and side slope is 2: 1. Using mid-sectional area method.a)480b)960c)1440d)1920Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the volume (cubic meter) of earthwork for an embankment of length 30 m and width 4 m. The mean depth of the embankment is 4 m and side slope is 2: 1. Using mid-sectional area method.a)480b)960c)1440d)1920Correct answer is option 'C'. Can you explain this answer?.
Calculate the volume (cubic meter) of earthwork for an embankment of length 30 m and width 4 m. The mean depth of the embankment is 4 m and side slope is 2: 1. Using mid-sectional area method.a)480b)960c)1440d)1920Correct answer is option 'C'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about Calculate the volume (cubic meter) of earthwork for an embankment of length 30 m and width 4 m. The mean depth of the embankment is 4 m and side slope is 2: 1. Using mid-sectional area method.a)480b)960c)1440d)1920Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Calculate the volume (cubic meter) of earthwork for an embankment of length 30 m and width 4 m. The mean depth of the embankment is 4 m and side slope is 2: 1. Using mid-sectional area method.a)480b)960c)1440d)1920Correct answer is option 'C'. Can you explain this answer?.
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