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Question
In a village, a well with 10 m inside diameter, is dug 14 m deep. Earth taken out of it is spread all around to a width 5 m to form an embankment. Find the height of the embankment. What value of the villagers is reflected here?
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Solution
We have,
Radius of well, R = `10/2` = 5 m,
Depth of the well, H = 14 m and
Width of the embarkment = 5 m,
Also, the outer radius of the embankment, r = R + 5 = 5 + 5 = 10 m
And , the inner radius of the embarkment = R = 5m
Let the height of the embankment = 5 m,
Also, the outer radius of the embankment, r = R + 5 = 5 + 5 = 10 m
And, the inner radius of the embankment = R = 5 m
Let the height of the embarkment be h.
Now,
Volume of the embankment = Volume of the earth taken out
⇒ Volume of embankment = Volume of the well
⇒ (πr2 - πR2) h = πR2H
⇒ π (r2 - R2) h = πR2H
⇒ (r2 - R2) h = R2H
⇒ (102 - 52) h = 5 × 5 × 14
⇒ (100 - 25) h = 25 × 14
⇒ 75 h = 25 × 14
`⇒ "h" = (25xx14)/75 `
`therefore "h" = 14/3 "m"`
So, the height of the embankment is `14/3` m
Value: We must lanour hard to make maximum use of the available resources.
Disclaimer: The answer provided in the textbook is incorrect. It has been corrected above.
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