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SanuByahut
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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 Answer

  1. Given,

    Inner radius of the well = 4 m

    Depth of the well = 14 m

    We know that,

    Volume of the cylinder = π r2h

    = π × 42 × 14 …. (i)

    From the question, it’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 = π (R2 – r2) × h

    = π × (72 – 42) × h …… (ii)

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

    π × 42 × 14 = π × (72 – 42) × h

    h = 42 × 14 / (33)

    h = 6.78 m

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

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