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Question
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?
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 = πr2h
= r ((1+x2)-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
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