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The number of cubic meters of the fill that can be constructed at a void ratio of 0.5 from 1000 m3 of borrow pit of soil that has a void ratio of 0.80 will be
  • a)
    500 m3
  • b)
    750 m3
  • c)
    833 m3
  • d)
    1000 m3
Correct answer is option 'C'. Can you explain this answer?
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The number of cubic meters of the fill that can be constructed at a vo...
 
Volume of solids remain same, 

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The number of cubic meters of the fill that can be constructed at a vo...
Given:
- Volume of borrow pit soil = 1000 m3
- Void ratio of borrow pit soil = 0.80
- Void ratio of fill to be constructed = 0.50

To find:
- Volume of fill that can be constructed

Formula:
- Void ratio = Volume of voids / Volume of solids
- Volume of voids = Void ratio * Volume of solids

Calculation:
- Volume of solids in borrow pit soil = Volume of borrow pit soil / (1 + void ratio) = 1000 / (1 + 0.80) = 555.56 m3
- Volume of voids in borrow pit soil = Void ratio * Volume of solids = 0.80 * 555.56 = 444.44 m3
- Volume of solids in fill = Volume of voids in borrow pit soil / (1 - void ratio of fill) = 444.44 / (1 - 0.50) = 888.89 m3
- Volume of fill = Volume of solids in fill + Volume of voids in fill = 888.89 + (0.50 * 888.89) = 1333.33 m3

Therefore, the volume of fill that can be constructed at a void ratio of 0.5 from 1000 m3 of borrow pit soil of soil that has a void ratio of 0.80 is 833 m3 (option C).
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The number of cubic meters of the fill that can be constructed at a void ratio of 0.5 from 1000 m3of borrow pit of soil that has a void ratio of 0.80 will bea)500 m3b)750 m3c)833 m3d)1000 m3Correct answer is option 'C'. Can you explain this answer?
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