Calculate Cost of Gold on Commemorative Quarter-Dollar

AI Thread Summary
To calculate the cost of gold on a commemorative quarter-dollar, the area of the coin is determined to be approximately 482.81 mm² using the formula for the area of a circle. The volume of the gold plating is calculated by multiplying the thickness of the gold layer (0.215 µm) by the area, resulting in a volume of about 103.80 mm³. To find the mass of the gold, the volume should be converted to grams using the density of gold, rather than dividing by the gold price. Participants suggest starting with the surface area calculation for one face of the coin to simplify the process. Understanding these calculations is essential for determining the cost of the gold added to the coin.
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1. Consider a commemorative quarter-dollar advertised for sale at $4.98. It has a diameter of 24.8 mm, a thickness of 1.78 mm, and is completely covered with a layer of pure gold 0.215 µm thick. The volume of the plating is equal to the thickness of the layer times the area to which it is applied. The patterns on the faces of the coin and the grooves on its edge have a negligible effect on its area. Assume the price of gold is $10.0 per gram. Find the cost of the gold added to the coin.i'm new at this. sorry if not posted correctly

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3. the area = (3.14)(12.4)(12.4)= 482.81
the volume = (.215)(482.81)= 103.80
i know i have to find how many grams there are now, but that's where I'm lost. Do i divide the volume by 10.0?
 
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You are supposed to make some attempt before you get help?
How about finding the surface area of the coin? You could start with one face.
 
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