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A well with inner radius 4 m is dug up and 14 m deep. Earth taken out of it has spread evenly all around a width of 3 m it to form an embankment. Find the height of the embankment?

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Given,

Inner radius of the well = 4 m

Depth of the well = 14 m

We know that,

Volume of the cylinder = π r2h

= π × 4× 14 …. (i)

From the question, it’s told that

The earth taken out from the well is evenly spread all around it to form an embankment

And, the width of the embankment = 3 m

So, the outer radius of the well = 3 + 4 m = 7 m

We know that,

Volume of the hollow embankment = π (R2 – r2) × h

= π × (72 – 42) × h …… (ii)

On equating both the equations (i) and (ii), we get

π × 4× 14 = π × (72 – 42) × h

h = 4× 14 / (33)

h = 6.78 m

Therefore, the height of the embankment so formed is 6.78 m.

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