Total Cost of Gold Plating is $621.58
Given
diameter of circular-disk earring = 4.0 cm
radius of circular-disk earring = 2.0 cm
thickness of gold coating = 0.25 mm
price of gold per troy ounce (31.10 g) = $1595
Now,
We calculate the volume of gold that is coated on one side of circular- disk earring .
hence,
Volume = π r² × width
= 3.14 × (2cm)²× (0.25 mm ×[tex]\frac{1cm}{10mm}[/tex])
= 0.314 cm³
Now,
Density of gold = 19.3 g/cm³
Now ,
Mass of gold deposited on one side of earring is
Mass = Density × Volume
= 19.3 g/cm³ × 0.314 cm³
= 6.06g
Similarly Mass of gold deposited on other side of earring is also 6.06g
Hence ,
Total mass of gold deposited on earring = 6.06 × 2
= 12.12g
Now given,
Price of gold per troy ounce (31.10g) = $1595
Price of 1 gram of gold = [tex]\frac{1595}{31.10}[/tex] =51.286$/g
Hence, Price of 12.12g gold = 51.286$/g ×12.12g
Price of 12.12g gold = $621.586
Thus from above conclusion , we can say that the total cost of gold plating is $621.586
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