# ML Aggarwal Solutions Class 10 Mathematics Solutions for Mensuration Exercise 17.5 in Chapter 17 - Mensuration

Question 16 Mensuration Exercise 17.5

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.

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 r2H

= π ×32×22

= 198 π m3

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 (R2– r2)h

= π (82– 32)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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