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Calculate the volume of the embankment (in cubic metre) using trapezoidal method, if the cross-section areas of the three sections of an embankment at an interval of 30 m are 20 square metres, 40 square metres and 50 square metres.
- a)1100
- b)1150
- c)2250
- d)2350
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Calculate the volume of the embankment (in cubic metre) using trapezoi...
Volume of embankment by trapezoidal method is given by:
V = h/2 [a1 + an + 2[a2 + a3 +…. an-1]
h = 30 m
a1 = 20 m2
a2 = 40 m2
a3 = 50 m2
V = 30/2[20 + 50 + 2[40]
V = 15 [150]
V = 2250 m3
Most Upvoted Answer
Calculate the volume of the embankment (in cubic metre) using trapezoi...
Given:
Cross-section areas of the embankment at an interval of 30 m = 20 m², 40 m², and 50 m²
To find:
The volume of the embankment using the trapezoidal method
Solution:
The trapezoidal method is used to calculate the volume of the embankment by dividing it into several trapezoidal sections and then adding their volumes.
Step 1: Find the average area of each trapezoidal section
Average area = (A1 + A2) / 2, where A1 and A2 are the cross-sectional areas at two adjacent intervals.
Therefore, the average area of the first section = (20 + 40) / 2 = 30 m²
The average area of the second section = (40 + 50) / 2 = 45 m²
Step 2: Find the distance between the two sections
Distance between the two sections = 30 m
Step 3: Calculate the volume of each trapezoidal section
Volume of a trapezoidal section = (1/2) x (A1 + A2) x distance
Therefore, the volume of the first trapezoidal section = (1/2) x (20 + 40) x 30 = 900 m³
The volume of the second trapezoidal section = (1/2) x (40 + 50) x 30 = 1350 m³
Step 4: Add the volumes of all the trapezoidal sections
Total volume = volume of first section + volume of second section
Total volume = 900 + 1350 = 2250 m³
Therefore, the volume of the embankment using the trapezoidal method is 2250 cubic metres.
Hence, the correct option is (C) 2250.
Cross-section areas of the embankment at an interval of 30 m = 20 m², 40 m², and 50 m²
To find:
The volume of the embankment using the trapezoidal method
Solution:
The trapezoidal method is used to calculate the volume of the embankment by dividing it into several trapezoidal sections and then adding their volumes.
Step 1: Find the average area of each trapezoidal section
Average area = (A1 + A2) / 2, where A1 and A2 are the cross-sectional areas at two adjacent intervals.
Therefore, the average area of the first section = (20 + 40) / 2 = 30 m²
The average area of the second section = (40 + 50) / 2 = 45 m²
Step 2: Find the distance between the two sections
Distance between the two sections = 30 m
Step 3: Calculate the volume of each trapezoidal section
Volume of a trapezoidal section = (1/2) x (A1 + A2) x distance
Therefore, the volume of the first trapezoidal section = (1/2) x (20 + 40) x 30 = 900 m³
The volume of the second trapezoidal section = (1/2) x (40 + 50) x 30 = 1350 m³
Step 4: Add the volumes of all the trapezoidal sections
Total volume = volume of first section + volume of second section
Total volume = 900 + 1350 = 2250 m³
Therefore, the volume of the embankment using the trapezoidal method is 2250 cubic metres.
Hence, the correct option is (C) 2250.
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Calculate the volume of the embankment (in cubic metre) using trapezoi...
C
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Calculate the volume of the embankment (in cubic metre) using trapezoidal method, if the cross-section areas of the three sections of an embankment at an interval of 30 m are 20 square metres, 40 square metres and 50 square metres. a)1100b)1150c)2250d)2350Correct answer is option 'C'. Can you explain this answer?
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