Calculate the value of the silver in the American Silver Eagle coin, assuming its thickness is uniform, given that it has a diameter of 41 mm, a thickness of 2.5 mm, a silver density of 10.5 g/cm3, and the approximate market price of silver is $0.51 per gram.

Verified step by step guidance

1. Convert the diameter and thickness of the coin from millimeters to centimeters to match the units of density. Remember that 1 cm = 10 mm.
2. Calculate the volume of the coin using the formula for the volume of a cylinder: \( V = \pi r^2 h \), where \( r \) is the radius and \( h \) is the height (thickness) of the cylinder.
3. Use the density formula \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \) to find the mass of the silver in the coin. Rearrange the formula to solve for mass: \( \text{Mass} = \text{Density} \times \text{Volume} \).
4. Calculate the mass of the silver in grams using the density of silver and the volume of the coin obtained in the previous steps.
5. Determine the value of the silver in the coin by multiplying the mass of the silver by the market price per gram of silver.