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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 Answer

  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 = π r2h

    = π × 12× 14 …. (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 = π × r2 × h

    = π × [(1 + x)2 – (1)2]× 0.4 ….. (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

    π × 12 × 14 = π × [(1 + x)2 – (1)2] x 0.4

    14/0.4 = 1 + x2 + 2x – 1

    35 = x2 + 2x

    x2 + 2x – 35 = 0

    Solving by factorization method, we have

    (x + 7) (x – 5) = 0

    So, x = 5 m can only be the solution as it’s a positive value.

    Therefore, the width of the embankment is 5 m.

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