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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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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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  1. ML Aggarwal Sol Class 10 Maths chapter 17-41

    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.

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