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14 August, 04:55

A sample of gold weighs 1.2 oz. The sample is pounded into a thin rectangular sheet with an area of 400. sq. ft. The density of gold is 19.3 grams per cm3. What is the thickness of the foil in centimeters? Given: 28.35 g = 1 oz, 1 ft = 12 inches, 1 inch = 2.54 cm

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  1. 14 August, 08:39
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    thickness of the gold sheet = 4.74 * 10⁻⁶ cm

    Explanation:

    mass of gold sample = 1.2 oz,; area of rectangular gold sheet = 400 sq. ft

    Converting mass of gold from oz. to g

    1 oz. = 28.35 g

    mass of gold sample in grams = 1.2 * 28.35 g = 34.02 g

    Converting from feet to cm;

    1 feet = 12 * 2.54 cm = 30.48 cm

    1 sq. ft = (30.48) ² = 929.0304 cm²

    area of gold in cm² = 400 * 929.0304 cm² = 371612.16 cm²

    Since the density of a solid is constant

    Density = mass/volume

    Volume = mass/density

    where volume = area * thickness

    therefore, area * thickness = mass/density

    thickness = mass / (density * area)

    substituting the value; thickness = 34.02 g / (19.3 gcm⁻³ * 371612.16 cm²)

    thickness of the gold sheet = 4.74 * 10⁻⁶ cm
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