Question

The U.S. Mint produces a dollar coin called the American Silver Eagle that is made of nearly pure silver. This coin has a diameter of 41 mm and a thickness of 2.5 mm. The density and approximate market price of silver are 10.5 g/cm3 and $0.51 per gram, respectively. Calculate the value of the silver in the coin, assuming its thickness is uniform.

Answer 1

The value of the silver in the coin is 35.3 $

Step-by-step explanation:

First of all, let's calculate the volume of the coin.

2π . r² . thickness = volume

r = diameter/2

r = 41 mm/2 = 20.5 mm

2 . π . (20.5 mm)² . 2.5 mm = 6601 mm³

Now, this is the volume of the coin, so we must find out how many grams are on it.

6601 mm³ / 1000 = 6.60 cm³

Let's apply density.

D = Mass / volume

10.5 g/cm³ = mass /6.60 cm³

10.5 g/cm³ . 6.60 cm³ = mass

69.3 g = mass

Each gram has a cost of 0.51$

69.3 g . 0.51$ = 35.3 $