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A well with inner diameter 6 m is dug 22 m deep. Soil taken out of it has been spread evenly all round it to a width of 5 m to form an embankment.

Find the height of the embankment.

Answer:

**Solution:**

The well is in cylindrical shape and the embankment will also be created in cylindrical shape around it.

Given inner diameter of the well = 6 m

Radius of the well, r = 6/2 = 3 m

Depth of the well, H = 22 m

Volume of the soil dug out of well = π r^{2}H

= π ×3^{2}×22

= 198 π m^{3}

Width of the embankment = 5 m

Inner radius of embankment, r = 3 m

Outer radius of embankment, R = 3+5 = 8 m

Let h be height of the soil embankment.

Volume of the soil embankment = π (R^{2}– r^{2})h

= π (8^{2}– 3^{2})h

=π (64-9)h

= 55π h

Volume of the soil dug out = volume of the soil embankment

198 π = 55π h

h = 198/55

h = 3.6 m

**Hence the height of the soil embankment is 3.6 m.**

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