Question

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?

Answer 1

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)

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 × 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.