Calculate Cost of Gold on Commemorative Quarter-Dollar

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SUMMARY

The discussion focuses on calculating the cost of gold on a commemorative quarter-dollar, priced at $4.98, with specific dimensions: a diameter of 24.8 mm and a thickness of 1.78 mm. The gold layer is 0.215 µm thick, leading to a calculated area of 482.81 mm² and a volume of 103.80 mm³. Given the gold price of $10.00 per gram, participants are guided to find the mass of gold by converting volume to grams, emphasizing the need to calculate the surface area accurately for precise cost estimation.

PREREQUISITES
  • Understanding of basic geometry, specifically area and volume calculations.
  • Familiarity with unit conversions, particularly between cubic millimeters and grams.
  • Knowledge of gold pricing and how to calculate costs based on weight.
  • Basic algebra skills to manipulate equations for solving problems.
NEXT STEPS
  • Learn about unit conversions between volume and mass, specifically for metals.
  • Study the formula for calculating the surface area of cylindrical objects.
  • Explore the properties of gold, including density and how it affects cost calculations.
  • Investigate methods for calculating costs of materials in collectible items.
USEFUL FOR

This discussion is beneficial for students in mathematics or engineering fields, collectors of commemorative coins, and anyone interested in the valuation of precious metals in collectibles.

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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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.