Question

The United States Has minted one dollar silver coins called American eagle silver bullion coins since 1986. Each coin has a diameter of 40.6 mm and is 2.98 mm thick. The density of silver is 10.5 g/cm³. Find the mass of an American eagle silver bullion coin.

Answer 1

The mass of an American eagle silver bullion coin is approximately 33.18 grams.

Step-by-step explanation:

To find the mass of an American eagle silver bullion coin, we need to calculate its volume and then multiply it by the density of silver.

The diameter of the coin is given as 40.6 mm and the thickness as 2.98 mm. We can assume the coin is a cylinder, so we'll use the formula for the volume of a cylinder: V =
`π(pi) r^2h`, where r is the radius and h is the height.

The radius is half the diameter, so r = 40.6 mm / 2 = 20.3 mm = 2.03 cm. Converting the thickness to cm, we get h = 2.98 mm / 10 = 0.298 cm.

Plugging in the values, we have
`V = π (pi)(2.03 cm)^2(0.298 cm)` = 3.16 cm³.

Finally, we multiply the volume by the density of silver, which is given as 10.5 g/cm³: mass = volume x density = 3.16 cm³ x 10.5 g/cm³ = 33.18 g.

The mass of an American eagle silver bullion coin is approximately 33.18 grams.