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Math Help - Density Problem

  1. #1
    Newbie
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    Sep 2007
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    Density Problem

    Hi. First time asking question here so sorry if format is wrong.

    Question:

    Gold leaf, which is used for many decorative purposes is made by hammering pure gold into very thin sheets. Assuming that a sheet of gold leaf is 1.27x10^-5 cm thick, how many square meters of gold leaf could be obtained from 28.35 g of gold.


    I know Density equals M/V and Volume equals M/D

    I've devised that 28.35 is the mass, but I don't know what the volume is, or what I'm even trying to find (Volume or Density? I'm guessing volume)

    All help welcome. Thanks a lot.
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    So density = mass/volume

    per internet search, density of gold = 19.3 grams/cu.cm
    That is 19.3 gm per 1 cm^3.

    One sheet of gold leaf is 0.0000127 cm thick.
    If this one sheet weighs 19.3 grams, what would be its area?
    (area in cm^2)*(0.0000127 cm) = 1 cm^3
    area = 1 /0.0000127 = 78,740 cm^2

    How many sq.m is that?
    (78,740 cm^2)(1 m^2 /(100cm)^2 = 7.874 m^2

    So, that means per 19.3 gm of gold, 7.874 m^2 of gold leaf can be made.

    There are 28.35 gm of gold to be made into gold leaf, so,
    (28.35 gm)(7.874m^2 /19.3 gm) = 11.566 m^2

    Therefore, 11.566 square meters of gold leaf can be obtained from 28.35 grams of gold. ---------answer.
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