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