An Important Question of class 10 Based on Mensuration Chapter of M.L Aggarwal for ICSE BOARD.
Here a well given with inner diameter 6 m is dug 22 m deep.
The 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.
This is the Question Number 14, Exercise 17.5 of M.L Aggarwal.
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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.
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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 = r2H
= ×32×22
= 198 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 = (R2– r2)h
= (82– 32)h
= (64-9)h
= 55h
Volume of the soil dug out = volume of the soil embankment
198 = 55h
h = 198/55
h = 3.6 m
Hence the height of the soil embankment is 3.6 m.