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Question

A well with inner radius 4 m is dug 14 m deep. Earth taken out of it has been spread evenly all around a width of 3 m it 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.

Given, r = 4 m and h = 14 m

Volume of earth dugged out of the wall=πr2h=π×42×14m

Let R and H be the outer radius and height of the embankment.

∴ R = Radius of the well + Width if the embankment = 4 cm + 3 cm = 7 cm

Volume of the earth in the embankment =π(R2r2)H=π(7242)H

Now, Volume of the earth in the embankment = Volume of earth dugged out of the wall

=>π(7242)h=π×42×14

=>(4916)h=16×14

=>h=22433=6.79 m

Thus, the height of the embankment is approximately 6.79 m.


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