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Question
A well with 10 m inside diameter is dug 8.4 m deep. Earth taken out of it is spread all around it to a width of 7.5 m to form an embankment. Find the height of the embankment.
Solution
Given data is as follows:
Inner diameter of the well = 10 m
Height = 8.4 m
Width of embankment = 7.5 m
We have to find the height of the embankment.
Given is the diameter of the well which is 10 m. Therefore,
r = 5 m
The outer radius of the embankment,
r = Inner radius of the well + width of the embankment
= 5 + 7.5
= 12.5 m
Let H be the height of the embankment.
The volume of earth dug out is equal to the volume of the embankment. Therefore,
Volume of embankment = Volume of earth dug out
`pi(R^2 - r^2) H = pir^2 h`
`22/7 xx (12.5^2-5^2) xx H = 22/7 xx 5 xx 5xx 8.4`
H = 1.6 m
Thus, height of the embankment is 1.6 m
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