A well of diameter 4 m is dug 14 m deep. The earth taken out of it is spread evenly all around the well to form a 40-cm-high embankment. Find the width the embankment.

Explanation

Radius of the well, r = 2 m.
Depth of the well, h = 14 m.
Volume of the earth taken out.
`=pir^(2)H=(22/7xx2xx2xx14)m^(3)=176 m^(3)`
Let the width of the embankment be x metres.
Internal radius of the embankment, R = (2+x) m.
Height of the embankment, `H=-40cm=(40/100)m`.
Volume of the embankment
`=piH(R^(2)-r^(2))={40/100[(2+x)^(2)-2^(2)1}m^(3)`
`=[(2pi)/5(x^(2)+4x)]m^(3)`.
Now, volume of the embankent = volume of hte earth dug out
? ltBRgt `rArr" "2/5xx22/7xx(x^(2)+4x)=176rArrx^(2)+4x=(176xx5xx7)/(2xx22)=140`
`rArr" "x(x+14)-10(x+14)=0rArr(x+14)(x-14)=0`
`rArr" "x=10" "[becausene-14]`.
Hence, width of the embankment = 10 m.