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# A well of diameter 2 m is dug 14 m deep. The earth taken out of it is evenly spread all around it to form an embankment of height 40 cm. Find the width of the embankment?

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I would like to give a question which
i could not solve.Rd sharma class 10
maths exercise-16.1 mensuration.

In this question we have to find the width of the
embankment of a well of diameter 2 m is dug 14 m deep.
The earth taken out of it is evenly spread all around it to
form an embankment of height 40 cm.

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1. Given,

Radius of the circular cylinder (r) = 2/2 m = 1 m

Height of the well (h) = 14 m

We know that,

Volume of the solid circular cylinder = Ï€ r2h

= Ï€ Ã— 12Ã— 14 â€¦. (i)

And,

The height of the embankment (h) = 40 cm = 0.4 m

Let the width of the embankment be (x) m.

The embankment is a hollow cylinder with external radius = 1 + x and internal radius = 1

Volume of the embankment = Ï€ Ã— r2 Ã— h

= Ï€ Ã— [(1 + x)2 â€“ (1)2]Ã— 0.4 â€¦.. (ii)

As the well is spread evenly to form embankment then the volumes will be same.

So, on equating equations (i) and (ii), we get

Ï€ Ã— 12 Ã— 14 = Ï€ Ã— [(1 + x)2 â€“ (1)2] x 0.4

14/0.4 = 1 + x2 + 2x â€“ 1

35 = x2 + 2x

x2 + 2x â€“ 35 = 0

Solving by factorization method, we have

(x + 7) (x â€“ 5) = 0

So, x = 5 m can only be the solution as itâ€™s a positive value.

Therefore, the width of the embankment is 5 m.

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