A well of diameter 3 m is dug 14 m deep. The earth taken out of it has been spread evenly all around it in the shape of a circular ring of width 4 m to form an embankment. Find the height of the embankment.

Given: Height of the well = 14 m

Diameter of the well = 3 m

To find: Height of embankment

Proof: Both well and embankment are in the form of cylinder

Let well be cylinder A and embankment be cylinder B

Since mud of well is distributed in embankment

⇒ Volume of Well = Volume of embankment

Firstly, we find the Volume of well:

Volume of the earth taken out of the well = πr²h

= 99 m³

So, Volume of well = 99m³

For Cylinder B

Outer radius = R = Inner radius + width

Volume of embankment = Volume of cylinder with outer Radius

– Volume of cylinder with inner radius

= πR²h – πr²h

= πh(R² – r²)

= πh(R – r)(R + r)

= 22 × 4 × h

= 88h m²

Volume of Well = Volume of embankment

⇒ 99 = 88h

⇒ h = 1.125m

Height of the embankment = 1.125 m