a well of diameter 3m dug 14m deep.The Earth taken out of it has been spread evenly all around it in the shape of a circular Ring of width 4m to form an embankment.find the height of the embankment.
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heroofcenturyp21f0g:
volume of ring is π(R^2-r^2)h
volume of soil which was dug is equals to the volume of ring
soil was dug in cylindrical shape so soil volume becomes the volume of cylinder
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Step-by-step explanation:
- Height of the well = 14 m.
- Diameter of the well = 3m.
- Therefore, Radius of the well = 3/2 m.
According to question now :
Volume of the earth taken out of the well = πr²h
=> 22/7 × 3/2 × 3/2 × 14
=> 22 × (3/2)² × 2
=> 44 × 9/4
=> 11 × 9
=> 99 cm.
Outer radius of embankment (R) = (3/2 +4)
=> 11/2 m
Now,
Area of embankment = outer area - inner area
=> πR² - πr²
=> 22/7 [(11/2)² - (3/2)²]
=> 22/7 × 112/4
=> 88 m²
Height of the embankment = Volume / Area
=> 99/88
=> 1.125 m
Therefore, the height of the embankment is 1.125 m
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