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# 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.

Let h be the required height of the embankment.

The shape of the embankment will be like the shape of a cylinder of internal radius 1.5 m and external radius $$4 \ + \ 1.5 \ = \ 5.5$$ m

The volume of the embankment will be equal to the volume of earth dug out from the well.

Now, the volume of the earth = Volume of the cylindrical well

$$= \ \pi \ × \ (1.5)^2 \ × \ 14 \ = \ 31.5\pi$$ m3

Also, the volume of the embankment

$$= \ \pi (5.52 \ - \ 1.52)h \ = \ \pi \ × \ 7 \ × \ 4h$$

$$= \ 28 \pi h$$ m3

$$\therefore 28 \pi h \ = \ 31.5 \pi$$

$$\Rightarrow \ h \ = \ \frac{31.5}{28} \ = \ 1.125$$ m

Hence, the required height of the embankment = 1.125 m