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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. 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.

Concept: Concept of Surface Area, Volume, and Capacity

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