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The boy having a gold coin of diameter 2cm and thickess 2mm to a goldsmith for melting and drawing into a wire of diameter 1mm . the gold smith gave back a wire of gold of length 76cm with diameter 1mm. if the wastage allowed in melting could be a maximum of 5% of the total volume , does the godsmith man was honest or not

  • maths-mensuration -

    If the smith was honest, you want

    pi (.05)^2 * 76 >= 0.95 pi (1)^2 * .2
    .19 >= .19

    Looks like the smith was honest.

  • maths-mensuration -

    from where .95 comes

  • maths-mensuration -

    5% waste means at least 95% of the metal must be left after working on it.

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