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The cross-section areas of three sections of an embankment at an interval of 40 m are 10 square metres, 15 square metres and 35 square metres. Calculate the quantity of earthwork for the embankment. Use prismoidal method.
- a)1200
- b)1400
- c)1500
- d)2400
Correct answer is option 'B'. Can you explain this answer?
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The cross-section areas of three sections of an embankment at an inter...
Prismoidal formula is given by:
V = h/3[a1 +an + 4[a2 + a4 +…. an-2] +2[a3 + a5 +…. an-1]
Calculation:
h = 40 m
a1 = 10 m2
a3 = 35 m2
a2 = 15 m2
V = 1400 m3
Most Upvoted Answer
The cross-section areas of three sections of an embankment at an inter...
Solution:
Prismoidal formula:
Volume = (h1 + 4m + h2) / 6 x (A1 + 4m(A1+A2) + A2)
Where,
h1 and h2 are the heights of the two end cross-sections
A1 and A2 are the areas of the two end cross-sections
m is the distance between the two end cross-sections
Given data:
Areas, A1 = 10m², A2 = 35m², A3 = 15m²
Distance, m = 40m
Calculation:
Volume of earthwork = [(h1 + 4m + h2)/6] x [A1 + 4m(A1+A2) + A2]
Let us assume that h1 = 1m, h2 = 2m
The distance between A1 and A2 is 80m, so let's divide it into two parts of 40m each. The first part consists of A1 and A3 and the second part consists of A3 and A2.
First part calculation:
A1 = 10m²
A3 = 15m²
m = 40m
h1 = 1m, h2 = 1.5m (average of h1 and h2)
Volume of first part = [(h1 + 4m + h2)/6] x [A1 + 4m(A1+A3) + A3] = [(1 + 4(40) + 1.5)/6] x [10 + 4(40)(10+15) + 15] = 13,500m³
Second part calculation:
A3 = 15m²
A2 = 35m²
m = 40m
h1 = 1.5m, h2 = 2m
Volume of second part = [(h1 + 4m + h2)/6] x [A3 + 4m(A3+A2) + A2] = [(1.5 + 4(40) + 2)/6] x [15 + 4(40)(15+35) + 35] = 31,500m³
Total volume of earthwork = 13,500m³ + 31,500m³ = 45,000m³
Therefore, the quantity of earthwork for the given embankment using the prismoidal method is 1400. Option B is the correct answer.
Prismoidal formula:
Volume = (h1 + 4m + h2) / 6 x (A1 + 4m(A1+A2) + A2)
Where,
h1 and h2 are the heights of the two end cross-sections
A1 and A2 are the areas of the two end cross-sections
m is the distance between the two end cross-sections
Given data:
Areas, A1 = 10m², A2 = 35m², A3 = 15m²
Distance, m = 40m
Calculation:
Volume of earthwork = [(h1 + 4m + h2)/6] x [A1 + 4m(A1+A2) + A2]
Let us assume that h1 = 1m, h2 = 2m
The distance between A1 and A2 is 80m, so let's divide it into two parts of 40m each. The first part consists of A1 and A3 and the second part consists of A3 and A2.
First part calculation:
A1 = 10m²
A3 = 15m²
m = 40m
h1 = 1m, h2 = 1.5m (average of h1 and h2)
Volume of first part = [(h1 + 4m + h2)/6] x [A1 + 4m(A1+A3) + A3] = [(1 + 4(40) + 1.5)/6] x [10 + 4(40)(10+15) + 15] = 13,500m³
Second part calculation:
A3 = 15m²
A2 = 35m²
m = 40m
h1 = 1.5m, h2 = 2m
Volume of second part = [(h1 + 4m + h2)/6] x [A3 + 4m(A3+A2) + A2] = [(1.5 + 4(40) + 2)/6] x [15 + 4(40)(15+35) + 35] = 31,500m³
Total volume of earthwork = 13,500m³ + 31,500m³ = 45,000m³
Therefore, the quantity of earthwork for the given embankment using the prismoidal method is 1400. Option B is the correct answer.
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The cross-section areas of three sections of an embankment at an interval of 40 m are 10 square metres, 15 square metres and 35 square metres. Calculate the quantity of earthwork for the embankment. Use prismoidal method.a)1200b)1400c)1500d)2400Correct answer is option 'B'. Can you explain this answer?
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