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4 June, 12:16

Precious metals and gems are measured in troy weights in the english system: 24 grains = 1 pennyweight (exact) 20 pennyweight = 1 troy ounce (exact) 12 troy ounces = 1 troy pound (exact) 1 grain = 0.0648 g 1 carat = 0.200 g

a. The most common english unit of math is the pound avoirdupois. What is 1 troy pound in kilograms and in pounds?

b. What is the mass of a troy ounce of gold in gram and in carats?

c. The density of gold is 19.3 g/cm 3. What is the volume of a troy pound of gold?

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  1. 4 June, 12:19
    0
    Given that

    24 grains = 1 pennyweight (exact)

    20 pennyweight = 1 troy ounce (exact)

    12 troy ounces = 1 troy pound (exact)

    1 grain = 0.0648 g

    1 carat = 0.200 g

    a) Mass of one troy pound in Kg and pounds

    (i) in kilograms

    1 troy pound = 12 troy ounces

    = 1 2X 20 penny weight

    = 12 X 20 X 24 grains

    = 12 X 20 X 24 X 0.0648 grams

    = 373.248 g

    =0.37325 Kg

    ii) in pounds

    1 gram = 0.002205 pounds

    373.248 g = 0.823 pounds

    b) 1 troy ounce = 20 penny weight

    = 20 X 24 grains

    = 20 X 24 X 0.0648 g

    = 31.104 g

    one carat = 0.20 g

    so 31.104g = 31.104 / 0.2 carot = 155.52 carat

    c) density of gold is 19.3 g/cm 3

    volume of 1 troy pound

    Mass of 1 troy pound in grams = 373. 248 g

    Volume = mass / density = 373.248 / 19.3 = 19.34 cm^3
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