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Question
A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to a width of 21 m to form an embankment. Find the height of the embankment.
Solution
Given data is as follows:
r = 7m
h = 8 m
R - r = 21 m
We have to find the height of the embankment.
Let the height of the embankment be H meter.
From the given data we have,
Volume of earth in embankment = Volume of earth dug out
Volume of embankment = `pi (R^2 - r^2)H`
Volume of earth dug out = `pir^2h`
Therefore, we have
`pi(R^2 - r^2) H = pir^2 h`
` (R^2 - r^2) H = r^2h`
`(R-r)(R+r)H=r^2h`
Here,
R - r = 21m
But,
r = 7 m
Therefore,
R - 7 = 21
R = 28 m
Substituting the values in the above equation, we have
`(28-7)(28+7)H=7xx7xx8`
`21xx35xxH = 7xx7xx8`
`H = 8/15 m`
= 0.533 m
= 53.3 cm
Therefore the height of the embankment is equal to 53.3 cm
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