To calculate the amount of air in bottles with varying vacuums measured in inches of mercury (in.hg), one can use the density ratios relative to atmospheric pressure, which is approximately 30 in.hg at sea level. For bottles with vacuums of 10 in.hg, 20 in.hg, and 30 in.hg, the air volume can be determined by comparing each vacuum level to the atmospheric pressure. The discussion emphasizes using these ratios to find the air density in each bottle. Understanding these calculations is crucial for accurate measurements in vacuum applications. This method provides a straightforward approach to quantify air content in vacuum conditions.