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A well with inner radius 4 m is dug 14 m deep. Earth taken out of it has been spread evenly all around a width of 3 m it to form an embankment. Find the height of the embankment.

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Let the height of the embankment be ‘h’ m 

Radius of well = 4 m 

Height of the well = 14 m 

Volume of earth dug out (volume of cylinder) = πr2h

\(\frac{22}7\times{4}\times{4}\times{14}\) m3

= 704 m3 

Outer Radius of the embankment(R) = 4 m + 3 m = 7 m 

Inner radius of the embankment(r) = 4 m 

Volume of embankment = Volume of earth dug out 

Volume of embankment = πR2h - πr2h

= πh (R2 – r2

= πh (72 – 42 ) 

= 33 πh 

Volume of embankment = Volume of earth dug out 

⇒ 33 πh = 704 

⇒ h = \(\frac{{704}\times{7}}{{33}\times{22}}\)

⇒ h = 6.78 m

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