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Question

Gold, which has a density of 19.32 g/cm3, is the most ductile metal and can be pressed into a thin leaf or drawn out into a long fiber.
If a sample of gold, with a mass of 27.60 g, is pressed into a leaf of 1.000 μm thickness, what is the area of the leaf?

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Solution

The density of gold is
ρ=mV=19.32 g1 cm3=19.32 g/cm3
We take the volume of the leaf to be its area A multiplied by its thickness z. With density ρ=19.32 g/cm3 and mass m=27.63 g, the volume of the leaf is found to be
V=mρ=1.430 cm3.
We convert the volume to SI units:
V=(1.430 cm3)(1 m100 cm)3=1.430×106m3
Since V=Az with z=1×106m (metric prefixes can be found in Table 12), we obtained

A=1.430×106m31×106m=1.430 m2

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