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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
Radius of well
`r = 10/2`
` = 5m`
Depth of well h = 8.4 m
Clearly,
Volume of earth dugout
`= pi(5)^2 xx 8.4`
`= pi xx 25 xx 8.4`
` =(22 xx 25 xx 8.4)/7 m^3`
Let h' be the height of embankment
Clearly,
Embankment forms a cylindrical shell whose inner and outer radius are 5 m and 12.5 m respectively.
∴ Volume of the embankment
`= pi{(12.5)^2 - (5)^2} xx h``
` = pi xx 17.5 xx 7.5 xx h' m^3`
But, volume of earth dugout = volume of the embankment
`(22 xx 25 xx 8.4)/7 = 22/7 xx 17.5 xx 7.5 xx h`
` h = (25 xx 8.4)/(17.5 xx 7.5)`
`h` = 1.6 m`
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