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 mRadius of the well, r = 6/2 = 3 mDepth of the well, H = 22 mVolume of the soil dug out of well = r^{2}H= Ã—3^{2}Ã—22= 198 m^{3}Width of the embankment = 5 mInner radius of embankment, r = 3 mOuter radius of embankment, R = 3+5 = 8 mLet h be height of the soil embankment.Volume of the soil embankment = (R^{2}â€“ r^{2})h= (8^{2}â€“ 3^{2})h= (64-9)h= 55hVolume of the soil dug out = volume of the soil embankment198 = 55hh = 198/55h = 3.6 mHence the height of the soil embankment is 3.6 m.