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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. - Mathematics

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.

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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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