A well of diameter 2m is dug14m deep. The earth taken out of it is spread evenly all around it to form an embankment of height 40cm. Find width of the embankment?

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#### Solution

Let us assume well as a solid circular cylinder

Radius of circular cylinder`=2/2=1m`

Height (or) depth of well = 14m

Volume of solid circular cylindeer =`pir^2h`

=π(1)^{2 }14 .........(1)

Given that height of embankment (h) = 40cm

Let width of embankment be ‘x’ m

Volume of embankment = πr^{2}h

= r ((1+x^{2})-1)^{2 }x 0.4 ...........(2)

Since well is spread evenly to form embankment so their volumes will be same so equating (1) and (2)

⇒ π(1)^{2 }x 14 = π((1+x)^{2} -1)^{2} x 0.4

⇒ x = 5m

∴Width of embankment of (x) = 5m

Concept: Volume of a Combination of Solids

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