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All the dimensions of the embankment were measured with 20 m chain and the volume was calculated as 368.85 cubic meter. It was then found that the chain was 10 cm too long. Find the true volume of embankment?
- a)374.4 m3
- b)494.3 m3
- c)368.8 m3
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
All the dimensions of the embankment were measured with 20 m chain and...
Given:
- Dimensions of the embankment were measured with a 20 m chain.
- The volume calculated was 368.85 cubic meters.
- The chain was found to be 10 cm too long.
To find:
The true volume of the embankment.
Solution:
1. Finding the actual length of the chain:
- The given chain is 20 m long.
- It was found to be 10 cm too long.
- Therefore, the actual length of the chain is 20 m - 0.1 m = 19.9 m.
2. Calculating the correction factor:
- The correction factor can be calculated using the formula:
Correction factor = (Measured length of the chain) / (Actual length of the chain)
- Substituting the values:
Correction factor = 20 m / 19.9 m = 1.005 m
3. Finding the corrected volume:
- The volume calculated using the measured dimensions is 368.85 cubic meters.
- To find the true volume, we can multiply the measured volume by the correction factor.
- True volume = Measured volume * Correction factor
= 368.85 cubic meters * 1.005
= 370.17925 cubic meters
≈ 370.18 cubic meters
4. Conclusion:
The true volume of the embankment is approximately 370.18 cubic meters, which is closest to option A) 374.4 cubic meters.
- Dimensions of the embankment were measured with a 20 m chain.
- The volume calculated was 368.85 cubic meters.
- The chain was found to be 10 cm too long.
To find:
The true volume of the embankment.
Solution:
1. Finding the actual length of the chain:
- The given chain is 20 m long.
- It was found to be 10 cm too long.
- Therefore, the actual length of the chain is 20 m - 0.1 m = 19.9 m.
2. Calculating the correction factor:
- The correction factor can be calculated using the formula:
Correction factor = (Measured length of the chain) / (Actual length of the chain)
- Substituting the values:
Correction factor = 20 m / 19.9 m = 1.005 m
3. Finding the corrected volume:
- The volume calculated using the measured dimensions is 368.85 cubic meters.
- To find the true volume, we can multiply the measured volume by the correction factor.
- True volume = Measured volume * Correction factor
= 368.85 cubic meters * 1.005
= 370.17925 cubic meters
≈ 370.18 cubic meters
4. Conclusion:
The true volume of the embankment is approximately 370.18 cubic meters, which is closest to option A) 374.4 cubic meters.
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Community Answer
All the dimensions of the embankment were measured with 20 m chain and...
Concept:
Correction for Erroneous Length of Chain/Tape:
- The chain surveying depends only on linear measurement of distances. For traversing only the errors in distance measurements are of importance and significance.
- Measuring devices either chain or tape can either be longer or shorter than the designated length.
- The measured distance will be smaller than the actual if the length of the chain is longer than the designated length.
- It will be larger than the actual if the chain is shorter than the designated length.
- The actual measured distance can be corrected by the following formula :
True or Correct Distance = L'/L x measured Distance
Where L' = Actual incorrect length of chain, and L = Designated length of chain
∴ True or correct Volume of ebankment = (L'/L)3 x Measured Volume of embankment
Where L' = Actual incorrect length of chain, and L = Designated length of chain
∴ True or correct Volume of ebankment = (L'/L)3 x Measured Volume of embankment
Given, L' = Actual incorrect length of chain = 20.1 m (as chain is 10 cm too long), L = Designated length of chain = 20 m, measured/calculated volume of embankment = 368.85 m3
∴ True or correct volume of embankment = (20.1/20)3 x 368.85 = 374.41 m3
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All the dimensions of the embankment were measured with 20 m chain and the volume was calculated as 368.85 cubic meter. It was then found that the chain was 10 cm too long. Find the true volume of embankment?a)374.4 m3b)494.3m3c)368.8m3d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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