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A road embankment 10 m wide at the formation level with side slopes 2:1 and with an average height of 5 m is constructed with an average gradient of 1:40 from the contour 220 m to 280 m. Find the volume of earthwork.
- a)6,40,000 m3
- b)1,40,000 m3
- c)3,40,000 m3
- d)2,40,000 m3
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A road embankment 10 m wide at the formation level with side slopes 2:...
To find the volume of earthwork for the road embankment, we need to calculate the cross-sectional area of the embankment and then multiply it by the length of the embankment.
Cross-Sectional Area of the Embankment:
- The embankment has a width of 10 m at the formation level.
- The side slopes are given as 2:1, which means for every 2 units of horizontal distance, the vertical distance is 1 unit.
- The average height of the embankment is 5 m.
- The average gradient of the embankment is 1:40, which means for every 1 unit of vertical distance, the horizontal distance is 40 units.
Calculating the Cross-Sectional Area:
1. Determine the horizontal distance at the formation level:
- The average gradient of 1:40 means for every 1 unit of vertical distance, the horizontal distance is 40 units.
- The contour difference from 220 m to 280 m is 280 m - 220 m = 60 m.
- The horizontal distance at the formation level is 40 times the vertical distance.
- So, the horizontal distance at the formation level is 40 * 60 m = 2400 m.
2. Calculate the cross-sectional area:
- The cross-sectional area of the embankment can be divided into two trapezoids, one for each side slope, and a rectangle for the formation level.
- The area of a trapezoid is given by the formula: (a + b) * h / 2, where a and b are the lengths of the parallel sides and h is the height.
- For the side slopes, the lengths of the parallel sides are the horizontal distance at the formation level and the height of the embankment.
- For the formation level, the length of the parallel sides is the width of the embankment.
- The cross-sectional area is the sum of the areas of the two trapezoids and the rectangle.
Calculating the Volume of Earthwork:
- The volume of earthwork is given by the formula: Volume = Area * Length.
- The length of the embankment is the contour difference from 220 m to 280 m, which is 280 m - 220 m = 60 m.
Hence, the correct answer is option 'D' - 2,40,000 m3.
Cross-Sectional Area of the Embankment:
- The embankment has a width of 10 m at the formation level.
- The side slopes are given as 2:1, which means for every 2 units of horizontal distance, the vertical distance is 1 unit.
- The average height of the embankment is 5 m.
- The average gradient of the embankment is 1:40, which means for every 1 unit of vertical distance, the horizontal distance is 40 units.
Calculating the Cross-Sectional Area:
1. Determine the horizontal distance at the formation level:
- The average gradient of 1:40 means for every 1 unit of vertical distance, the horizontal distance is 40 units.
- The contour difference from 220 m to 280 m is 280 m - 220 m = 60 m.
- The horizontal distance at the formation level is 40 times the vertical distance.
- So, the horizontal distance at the formation level is 40 * 60 m = 2400 m.
2. Calculate the cross-sectional area:
- The cross-sectional area of the embankment can be divided into two trapezoids, one for each side slope, and a rectangle for the formation level.
- The area of a trapezoid is given by the formula: (a + b) * h / 2, where a and b are the lengths of the parallel sides and h is the height.
- For the side slopes, the lengths of the parallel sides are the horizontal distance at the formation level and the height of the embankment.
- For the formation level, the length of the parallel sides is the width of the embankment.
- The cross-sectional area is the sum of the areas of the two trapezoids and the rectangle.
Calculating the Volume of Earthwork:
- The volume of earthwork is given by the formula: Volume = Area * Length.
- The length of the embankment is the contour difference from 220 m to 280 m, which is 280 m - 220 m = 60 m.
Hence, the correct answer is option 'D' - 2,40,000 m3.
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Community Answer
A road embankment 10 m wide at the formation level with side slopes 2:...
Gradient:
A gradient is the rate of rise or falls along the length of the road with respect to horizontal. It is expressed as ‘1' vertical unit to 'N' horizontal units.
Area of trapezoidal:
According to the trapezoid area formula, the area of a trapezoid is equal to half the product of the height and the sum of the two bases.
Area = ½ x (Sum of parallel sides) x (perpendicular distance between the parallel sides).
Calculation:
Road embankment = 10 m
Average height = 5 m
Difference in elevation(h) = 280 - 220 = 60 m
Average gradient = 1/40
A gradient is the rate of rise or falls along the length of the road with respect to horizontal. It is expressed as ‘1' vertical unit to 'N' horizontal units.
Area of trapezoidal:
According to the trapezoid area formula, the area of a trapezoid is equal to half the product of the height and the sum of the two bases.
Area = ½ x (Sum of parallel sides) x (perpendicular distance between the parallel sides).
Calculation:
Road embankment = 10 m
Average height = 5 m
Difference in elevation(h) = 280 - 220 = 60 m
Average gradient = 1/40
Average cross-sectional area(A) = (1/2) ×(10+30)×5
A = 100 m2
Volume of earthwork = A × L
Volume of earthwork = 100 × 2400
∴ Volume of earthwork = 2,40,000 m3
A = 100 m2
Volume of earthwork = A × L
Volume of earthwork = 100 × 2400
∴ Volume of earthwork = 2,40,000 m3
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A road embankment 10 m wide at the formation level with side slopes 2:1 and with an average height of 5 m is constructed with an average gradient of 1:40 from the contour 220 m to 280 m. Find the volume of earthwork.a)6,40,000 m3b)1,40,000 m3c)3,40,000 m3d)2,40,000 m3Correct answer is option 'D'. Can you explain this answer?
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A road embankment 10 m wide at the formation level with side slopes 2:1 and with an average height of 5 m is constructed with an average gradient of 1:40 from the contour 220 m to 280 m. Find the volume of earthwork.a)6,40,000 m3b)1,40,000 m3c)3,40,000 m3d)2,40,000 m3Correct answer is option 'D'. 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 A road embankment 10 m wide at the formation level with side slopes 2:1 and with an average height of 5 m is constructed with an average gradient of 1:40 from the contour 220 m to 280 m. Find the volume of earthwork.a)6,40,000 m3b)1,40,000 m3c)3,40,000 m3d)2,40,000 m3Correct answer is option 'D'. 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 A road embankment 10 m wide at the formation level with side slopes 2:1 and with an average height of 5 m is constructed with an average gradient of 1:40 from the contour 220 m to 280 m. Find the volume of earthwork.a)6,40,000 m3b)1,40,000 m3c)3,40,000 m3d)2,40,000 m3Correct answer is option 'D'. Can you explain this answer?.
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