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Calculate the quantity of earthwork for 200 m length for a portion of road in an uniform ground the heights of banks at the two ends being 1.00 m and 1.60 m. The formation width is 10 mm and side slope 2:1. Assume that there is no traverse slope.
  • a)
    3276 cu m
  • b)
    5676 cu m
  • c)
    6757 cu m
  • d)
    1121 cu m
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Calculate the quantity of earthwork for 200 m length for a portion of ...
To calculate the quantity of earthwork for a portion of road, we need to consider the heights of the banks at the two ends, the formation width, and the side slope. Let's break down the calculations step by step:

Given data:
- Length of road portion = 200 m
- Height of bank at one end = 1.00 m
- Height of bank at the other end = 1.60 m
- Formation width = 10 m
- Side slope = 2:1

Calculations:
1. Calculate the average height of the banks:
Average height = (Height of bank at one end + Height of bank at the other end) / 2
Average height = (1.00 + 1.60) / 2 = 1.30 m

2. Calculate the height of the formation level:
Formation level height = Average height - (Formation width / 2)
Formation level height = 1.30 - (10 / 2) = 1.30 - 5 = -3.70 m

Note: The negative sign indicates that the formation level is below the ground level.

3. Calculate the cross-sectional area of earthwork:
Cross-sectional area = (Formation width + 2 * Side slope * Formation level height) * Length
Cross-sectional area = (10 + 2 * (2/1) * (-3.70)) * 200
Cross-sectional area = (10 + 2 * 4 * (-3.70)) * 200
Cross-sectional area = (10 + 8 * (-3.70)) * 200
Cross-sectional area = (10 - 29.60) * 200
Cross-sectional area = (-19.60) * 200
Cross-sectional area = -3920 m²

Note: The negative sign indicates that the cross-sectional area is below the ground level.

4. Calculate the volume of earthwork:
Volume = Cross-sectional area * Length
Volume = -3920 * 200
Volume = -784,000 m³

Note: The negative sign indicates that the volume is below the ground level.

5. Adjust the volume to account for the negative sign:
Positive volume = |Volume|
Positive volume = |-784,000|
Positive volume = 784,000 m³

Therefore, the quantity of earthwork for a 200 m length portion of road is 784,000 m³. However, the given options do not match the calculated result. Please double-check the calculations or provide additional information if necessary.
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Community Answer
Calculate the quantity of earthwork for 200 m length for a portion of ...
Quantity = (Bd+sd2) *length
Where, B=10 m, S=2, L=200 m, d=mean depth = (1+1.60)/2 = 1.30 m
Quantity = (10*1.3+2*1.32)*200 = (13=3.38)*200 = 16.38*200 = 3276 cu m.
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Calculate the quantity of earthwork for 200 m length for a portion of road in an uniform ground the heights of banks at the two ends being 1.00 m and 1.60 m. The formation width is 10 mm and side slope 2:1. Assume that there is no traverse slope.a)3276 cu mb)5676 cu mc)6757 cu md)1121 cu mCorrect answer is option 'A'. Can you explain this answer?
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