To determine if the rings are pure silver, we can calculate the density of the rings and compare it to the density of pure silver. The density of a material is the mass of the material per unit volume.
First, we need to find the volume of one of the rings. Since the rings are cylindrical, we can use the formula for the volume of a cylinder to find the volume of each ring:
V = π * r^2 * h
Where V is the volume of the ring, π is approximately equal to 3.14, r is the radius of the ring, and h is the height of the ring. In this case, the height of the ring is equal to the thickness of the ring, which is equal to the change in the water level (8.45 mm) divided by the number of rings (10). The radius of the ring is equal to half the diameter of the graduated cylinder (2.5 cm / 2 = 1.25 cm), since the rings are placed in the cylinder side by side.
Plugging these values into the formula, we find that the volume of each ring is:
V = 3.14 * (1.25 cm)^2 * (8.45 mm / 10) = 0.00367 cm^3
Next, we can use the mass and volume of each ring to calculate the density of the rings:
density = mass / volume
Since the mass of each ring is 0.738g and the volume of each ring is 0.00367 cm^3, the density of the rings is:
density = 0.738 g / 0.00367 cm^3 = 201.09 g/cm^3
Finally, we can compare the density of the rings to the density of pure silver, which is 10.49 g/cm^3. Since the density of the rings is much higher than the density of pure silver, it is likely that the rings are not pure silver.
It is important to note that this calculation is only an approximate estimation of the purity of the rings. There may be other factors that affect the density of the rings, such as impurities or variations in the thickness of the rings. Additionally, the value of the density of pure silver used in this calculation may not be entirely accurate, as the density of a material can vary depending on factors such as temperature and pressure. A more precise determination of the purity of the rings would require further testing and analysis.