Question

A well of diameter 3 m is dug 21 m deep. The earth taken out of it is spread evenly all around it to a width of 4 m to form an embankment, find the height of embankment.

Answer 1

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Answer 2

Answer:-

Given:-

Inner radius of the well = 4 m

Depth of the well = 14 m

We know that:-

Volume of the cylinder = π r2h

= π × 42 × 14 …. (i)

According to question:-

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 × 42 × 14 = π × (72 – 42) × h

h = 42 × 14 / (33)

h = 6.78 m

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