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# A well of diameter 3 m is dug up to 14 m deep. The earth taken out of it has been spread evenly all around it to a width of 4 m to form an embankment. Find the height of the embankment.

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If you open math book you will find a lot of mathematical questions but
youshould have solve this question.
It is from class 10 rd sharma chapter 16 mensuration .

In this question we have to find the height of the embankment.
Given that,
a well of diameter 3 m is dug up to 14 m deep. The earth taken
out of it has been spread evenly all around it to a width of 4 m
to form an embankment.

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1. Given,

Diameter of the well = 3 m

So, the radius of the well = 3/2 m = 1.5 m

Depth of the well (h) = 14 m

Width of the embankment (thickness) = 4 m

So, the radius of the outer surface of the embankment = (4 + 1.5) m = 5.5 m

Let the height of the embankment be taken as h m

We know that the embankment is a hollow cylinder

Volume of the embankment = Ï€ (R2 â€“ r2) Ã— h

= Ï€ (5.52 â€“ 1.52) Ã— h â€¦.. (i)

Volume of earth dug out = Ï€ Ã— r2 Ã— h

= Ï€ Ã— 22 Ã— 14 â€¦.. (ii)

On equating both (i) and (ii) we get,

Ï€ (5.52 â€“ 1.52) Ã— h = Ï€ Ã— (3/2)2 Ã— 14

(30.25 â€“ 2.25) x h = 9 x 14/ 4

h = 9 x 14/ (4 x 28)

h = 9/8 m

Therefore, the height of the embankment is 9/8 m

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