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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 Answer

  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 = π (R2 – r2) × h

    = π (5.52 – 1.52) × h ….. (i)

    Volume of earth dug out = π × r2 × h

    = π × 22 × 14 ….. (ii)

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

    π (5.52 – 1.52) × h = π × (3/2)2 × 14

    (30.25 – 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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