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

Given, Depth of well = 14 m, radius = 2 m.

Volume of earth taken out = πr2h

Let h be the height of a well and r be the radius of well

h=14m,r=d/2=2m

Volume of earth taken out after digging the well= pi × r2 × h

=((22/7) × 2 × 2 × 14)m3=176m3

Let x be the width of embankment formed by using(i)

Total width of well including embankment (R)=2+x

Height of embankment(H)=40cm=40/100 m

Volume of well=Volume of embankment

So,

Volume of embankment=pi × (R2-r2)H=176

=22/7[(2+x)2-(2)2] × 40/100=176

44/35[x2+4x]=176

44x2+176x=6160

x2 + 14x – 10x-140=0

x(x + 14)-10(x+14)=0

(x + 14)(x-10)=0

X + 14=0 or x-10=0

X=-14 or x=10

Therefore,width of embankment=10m

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