Final answer:
To find a hydrometer's volume, use the mass and density of air, and apply Archimedes' Principle to determine the submerged volume for the stern's length above water.
Step-by-step explanation:
To determine the total volume of a hydrometer, it is important to understand the concept of buoyancy, which is the principle that a hydrometer works on. The hydrometer floats in a fluid, and depending on its density, the submerged volume can be used to calculate the density of the liquid. In the case of air, the entire hydrometer would be submerged, and given the data provided, where the mass of the hydrometer is 19g and the density of air is 1.2g/cm³, we can use the relation V = m/ρ to find the volume of the hydrometer. Since the cross-sectional area is given in square meters, it needs to be converted to square centimeters for consistency with the density units.
1) The total volume (V) of the hydrometer: V = m/ρ = 19g / 1.2g/cm³ = 15.83cm³.
2) For the length of the stern above water, we apply Archimedes' Principle, which shows that the volume of fluid displaced will equal the volume of the submerged part of the hydrometer, given by a cross-sectional area times submerged height. Given the density of water is 1g/cm³ and the hydrometer is floating, so the submerged volume equals the mass of the hydrometer. Therefore the submerged volume Vsubmerged = 19cm³. If A is the cross-sectional area in cm², and h is the submerged length, then Vsubmerged = Ah => h = Vsubmerged / A. Once A is converted and h is calculated, the total length of the stern L will be height above water plus submerged height.