According to the United States Mint, the “American Eagle Gold Bullion Coins” all consist of 22 carat gold. The dimensions and masses of the $5 and $50 Gold Bullion coins are as follows:
| Coin | Diameter (mm) +/- 0.01mm | Thickness (mm) +/-0.01mm | Mass (g) +/- 0.0005g |
| $5 | 16.50 | 1.26 | 3.393 |
| $50 | 32.70 | 2.87 | 33.931 |
One might have thought that – given both are 22 carat gold – the density of the coins would be identical. But careful calculation shows that their densities are not identical. Your task is to determine whether the variation in density is significant.
REPORT YOUR FINAL VALUES TO FOUR SIGNIFICANT FIGURES
Volume of cylinder: V=Pi.r^2.h
V=3.141592653 X (16.5/2)^2 X 1.26=269.419mm^3 volume of $5 coin,
269.419/1000=.269419cm^3
Density=3.393/.269419=12.594gm/cm^3 density of $5 coin.
V=3.141592653 X (32.70/2)^2 X 2.87=2,410.279mm^3 volume of $50 coin,
2,410.279/1000=2.410279cm^3
Density=33.931/2.410279=14.078gm/cm^3 density of $50 coin
The $50 coin is denser by about 1.5gm/cm^3. So, the difference in density is significant despite the uncertainty given in the table. There is no overlapping uncertainty.
