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If cross sectional area of an embankment at 30 m intervals are 20, 40, 60, 50 and 30 m2 respectively, then volume of the embankment on the basis of prismoidal rule is:
- a)5300 m2
- b)8300 m2
- c)4300 m2
- d)6300 m2
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
If cross sectional area of an embankment at 30 m intervals are 20, 40,...
Volume of embankment is given by:
d = 30 m
A1 = 20 m2
A2 = 40 m2
A3 = 60 m2
A4 = 50 m2
A5 = 30 m2
Most Upvoted Answer
If cross sectional area of an embankment at 30 m intervals are 20, 40,...
Calculation of Volume using Prismoidal Rule
Given:
Cross-sectional area of the embankment at 30 m intervals = 20, 40, 60, 50 and 30 m²
Step 1: Calculation of Mean Area
Mean area of the embankment can be calculated using the following formula:
Mean area = (A1 + 4A2 + A3) / 6
Where,
A1 = Area at the first station
A2 = Area at the middle station
A3 = Area at the last station
Therefore,
Mean area = (20 + 4(60) + 30) / 6
Mean area = 50 m²
Step 2: Calculation of End Areas
End areas can be calculated using the following formula:
End area = (A1 + A3 + 4A2) / 6
Where,
A1 = Area at the first station
A2 = Area at the middle station
A3 = Area at the last station
Therefore,
End area at the first station = (20 + 30 + 4(40)) / 6
End area at the first station = 36.67 m²
End area at the last station = (20 + 30 + 4(50)) / 6
End area at the last station = 40 m²
Step 3: Calculation of Volume
Volume of the embankment can be calculated using the prismoidal formula:
Volume = (L / 6) x (A1 + 4Am + An + 2Em)
Where,
L = Length of the embankment
Am = Mean area
A1 = Area at the first station
An = Area at the last station
Em = End area
Therefore,
Length of embankment = (30 x 4) = 120 m
Volume = (120 / 6) x (36.67 + 4(50) + 40 + 2(20 + 60 + 50))
Volume = 5300 m³
Therefore, the volume of the embankment on the basis of prismoidal rule is 5300 m³.
Given:
Cross-sectional area of the embankment at 30 m intervals = 20, 40, 60, 50 and 30 m²
Step 1: Calculation of Mean Area
Mean area of the embankment can be calculated using the following formula:
Mean area = (A1 + 4A2 + A3) / 6
Where,
A1 = Area at the first station
A2 = Area at the middle station
A3 = Area at the last station
Therefore,
Mean area = (20 + 4(60) + 30) / 6
Mean area = 50 m²
Step 2: Calculation of End Areas
End areas can be calculated using the following formula:
End area = (A1 + A3 + 4A2) / 6
Where,
A1 = Area at the first station
A2 = Area at the middle station
A3 = Area at the last station
Therefore,
End area at the first station = (20 + 30 + 4(40)) / 6
End area at the first station = 36.67 m²
End area at the last station = (20 + 30 + 4(50)) / 6
End area at the last station = 40 m²
Step 3: Calculation of Volume
Volume of the embankment can be calculated using the prismoidal formula:
Volume = (L / 6) x (A1 + 4Am + An + 2Em)
Where,
L = Length of the embankment
Am = Mean area
A1 = Area at the first station
An = Area at the last station
Em = End area
Therefore,
Length of embankment = (30 x 4) = 120 m
Volume = (120 / 6) x (36.67 + 4(50) + 40 + 2(20 + 60 + 50))
Volume = 5300 m³
Therefore, the volume of the embankment on the basis of prismoidal rule is 5300 m³.
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Community Answer
If cross sectional area of an embankment at 30 m intervals are 20, 40,...
Volume= h/3(A1+An+4(A2+A4+...)+2(A3+A5..))
=30/3(20+30+4(40+50)+2*60))=5300 m3
=30/3(20+30+4(40+50)+2*60))=5300 m3
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If cross sectional area of an embankment at 30 m intervals are 20, 40, 60, 50 and 30 m2respectively, then volume of the embankment on the basis of prismoidal rule is:a)5300 m2b)8300 m2c)4300 m2d)6300 m2Correct answer is option 'A'. Can you explain this answer?
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