Calculate Cost of Gold on Commemorative Quarter-Dollar

[r.anthony]

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

Homework Equations

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?

 

[Delphi51]

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.

 

[nlightner]

To find the cost of the gold added to the coin, you first need to calculate the mass of the gold plating. This can be done by converting the volume of the plating into mass using the density of gold, which is 19.3 g/cm³. The formula for this conversion is:

mass = volume x density

So, in this case, the mass of the gold plating would be:

mass = 103.80 cm³ x 19.3 g/cm³ = 2,003.74 g

Next, you need to convert the mass into grams. Since the price of gold is given in grams, this step is not necessary.

Finally, to calculate the cost of the gold, you simply multiply the mass by the price per gram:

cost = 2,003.74 g x $10.0/g = $20,037.4

Therefore, the cost of the gold added to the coin is $20,037.4. This is the additional cost on top of the base price of $4.98 for the commemorative quarter-dollar.