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For calculation of volume of earthwork, which of the following formulas assumes that short lengths in parabolic arcs are considered as parallel to each other?
- a)Average area formula
- b)Mid-section formula
- c)Trapezoidal rule formula
- d)Simpson’s rule formula
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
For calculation of volume of earthwork, which of the following formula...
Simpson's method assumes that the short lengths of the boundaries between the ordinates are parabolic arcs. This method is more useful when the boundary line departs considerably from the straight line.
Earthwork computation is involved in the excavation of channels, digging of trenches for laying underground pipelines, formation of bunds, and earthen embankments, digging of farm ponds, land leveling, and smoothening. In most of the computation, the cross-sectional areas at different interval along the length of the channels and embankments are first calculated and the volume of the prismoids are obtained between successive cross-section either by trapezoidal or prismoidal formula.
Calculation of area is carried out by any one of the following methods:
(a) Mid-ordinate method
(b) Average ordinate method
(c) Trapezoidal rule
(d) Simpson’s rule
Trapezoidal Rule
Earthwork computation is involved in the excavation of channels, digging of trenches for laying underground pipelines, formation of bunds, and earthen embankments, digging of farm ponds, land leveling, and smoothening. In most of the computation, the cross-sectional areas at different interval along the length of the channels and embankments are first calculated and the volume of the prismoids are obtained between successive cross-section either by trapezoidal or prismoidal formula.
Calculation of area is carried out by any one of the following methods:
(a) Mid-ordinate method
(b) Average ordinate method
(c) Trapezoidal rule
(d) Simpson’s rule
Trapezoidal Rule
- Boundaries of the ordinates are presumed to be straight. Therefore the area between the lines is considered to be a trapezoid.
This rule can be used for any number of ordinates, and hence it has no drawbacks or limitations.
Simpson’s Rule:
- An arc is assumed to be present between the boundaries of the ordinates. Therefore it is also known as the parabolic rule.
Additional Information
- The only limitation to this rule is that it can only be used when the number of ordinates is odd.
- Simpson’s rule gives a more accurate result.
- After the calculation of the cross-sectional areas, volume is also needed to be calculated to determine the capacity
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For calculation of volume of earthwork, which of the following formula...
C) Trapezoidal rule formula
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For calculation of volume of earthwork, which of the following formulas assumes that short lengths in parabolic arcs are considered as parallel to each other?a)Average area formulab)Mid-section formulac)Trapezoidal rule formulad)Simpson’s rule formulaCorrect answer is option 'D'. Can you explain this answer?
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