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# A well with inner radius 4 m is dug up and 14 m deep. Earth taken out of it has spread evenly all around a width of 3 m it to form an embankment. Find the height of the embankment?

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This question is from r d sharma class 10 maths.
I found this question while doing maths class 10.
I need help in getting the solution.

In this question we have to find the height of the embankment
from a well with inner radius 4 m is
dug up and 14 m deep. Earth taken out of it has spread evenly
all around a width of 3 m it to form an embankment.

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1. Given,

Inner radius of the well = 4 m

Depth of the well = 14 m

We know that,

Volume of the cylinder = Ï€ r2h

= Ï€ Ã— 42 Ã— 14 â€¦. (i)

From the question, itâ€™s told that

The earth taken out from the well is evenly spread all around it to form an embankment

And, the width of the embankment = 3 m

So, the outer radius of the well = 3 + 4 m = 7 m

We know that,

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

= Ï€ Ã— (72 â€“ 42) Ã— h â€¦â€¦ (ii)

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

Ï€ Ã— 42 Ã— 14 = Ï€ Ã— (72 â€“ 42) Ã— h

h = 42 Ã— 14 / (33)

h = 6.78 m

Therefore, the height of the embankment so formed is 6.78 m.

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