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Question
A well of diameter 4 m is dug 21 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 3 m to form an embankment. Find the height of the embankment.
Solution
Let r and h be the radius and depth of the well, respectively.
`:.r=4/2=2m ` and h = 21 m
Let R and H be the outer radius and height of the embankment, respectively.
∴ R = r + 3 = 2 + 3 = 5 m
Now
Volume of the earth used to form the embankment = Volume of the earth dug out of the well
`pi(R^2-r^2)H=pir^2h`
`=>H=(r^2h)/(R^2-r^2)`
`=>H=(2^2xx21)/(5^2-2^2)=4m`
Thus, the height of the embankment is 4 m.
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