Calculate Cost of Gold on Commemorative Quarter-Dollar

In summary, the commemorative quarter-dollar for sale is priced at $4.98 and has a diameter of 24.8 mm and a thickness of 1.78 mm. It is covered with a layer of pure gold 0.215 µm thick, which has a volume of 103.80 µm. Assuming a price of $10.0 per gram, the cost of the gold added to the coin can be found by dividing the volume by 10.0. To find the surface area of the coin, we can start by calculating the area of one face using the formula (3.14)(12.4)(12.4)= 482.81.
  • #1
r.anthony
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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

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?
 
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  • #2
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.
 
  • #3

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.
 

Related to Calculate Cost of Gold on Commemorative Quarter-Dollar

1. How is the cost of gold on a commemorative quarter-dollar calculated?

The cost of gold on a commemorative quarter-dollar is calculated by taking into account the current market price of gold, the weight of the quarter-dollar, and any additional costs such as production and minting fees. This calculation is typically done by the government agency responsible for producing the commemorative quarter-dollar.

2. What factors influence the cost of gold on a commemorative quarter-dollar?

The cost of gold on a commemorative quarter-dollar is influenced by several factors including the current market price of gold, the weight and purity of the gold used, and any additional production and minting costs. The demand for commemorative quarter-dollars can also impact the cost of gold on these coins.

3. How often is the cost of gold on a commemorative quarter-dollar updated?

The cost of gold on a commemorative quarter-dollar is typically updated on a regular basis, as the market price of gold can fluctuate daily. The government agency responsible for producing the commemorative quarter-dollar will usually monitor the market and update the cost accordingly.

4. Is the cost of gold on a commemorative quarter-dollar the same as the value of the coin?

No, the cost of gold on a commemorative quarter-dollar is not the same as the value of the coin. The cost of gold is only one factor in determining the value of a commemorative quarter-dollar. Other factors such as rarity, condition, and collector demand also play a role in determining the overall value of the coin.

5. Can individuals purchase commemorative quarter-dollars at the cost of gold?

No, commemorative quarter-dollars are not typically sold at the cost of gold. The government agency responsible for producing the coins will usually sell them at a higher price to cover production and minting costs, as well as to generate revenue. However, the cost of gold is still an important factor in determining the selling price of commemorative quarter-dollars.

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