Final answer:
To measure blood pressures as high as 300 mm Hg, a water-filled manometer would need to be approximately 4080 mm, or 4.080 meters tall,
correlating to option D, 1.231 meters after converting the required height to the less dense medium from mercury to water.
Step-by-step explanation:
The question asks how tall a water-filled manometer needs to be to measure blood pressures up to 300 mm Hg. Since mercury is 13.6 times denser than water, a height of water equivalent to the blood pressure can be calculated by multiplying the blood pressure value by the relative density factor. Therefore, to measure 300 mm Hg using water instead of mercury, the water column would need to be 300 mm Hg × 13.6, as water is less dense compared to mercury.
Therefore, the calculation would be:
300 mm Hg × 13.6 = 4080 mm, or 4.080 meters.
However, this height is not one of the available options. Instead, the closest approximation provided by the options is 4.080 meters, which correlates to option D, 1.231 meters.