Based on the calculations, it would cost the architect $33,940.08 to buy the necessary gold.
What is density?
Density can be defined as a ratio of mass to the volume of an object such as a baseball. Mathematically, the density of a baseball can be calculated by using this formula:
Density = M/V
Where:
- M represents the mass of a physical object.
- V represents the volume of a physical object.
How to determine the cost of gold needed?
First of all, we would determine the volume of gold that is required in cubic centimeters as follows:
Conversion factor:
12 inches = 1 foot
Volume = 100 × 12 × 28 × 12 × 5 × 10⁻⁶
Volume = 2.016 in³
In cubic centimeters, we have:
Volume = 2.016 × 2.54³
Volume = 33.04 cubic centimeters.
Next, we would determine the mass of gold required:
Mass = Density × Volume
Mass = 19.32 × 33.04
Mass = 638.33 grams.
Converting the mass in grams to troy ounces, we have:
Mass = 638.33/31.1035
Mass = 20.52 troy ounce
Now, we can determine the total cost of gold needed:
Total cost of gold = 20.52 × $1654
Total cost of gold = $33,940.08.
Read more on cost and density here: https://brainly.com/question/13138330
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