To measure density precisely, especially under water, an accurate method for determining volume is essential, as mass can be easily measured. Pycnometers are commonly used for measuring the volume of liquids and solids, with specific devices available for each type. For solids, Archimedes' principle can be applied by submerging the sample in water and measuring the displaced volume, which can yield about 1% accuracy. Alternative methods, such as measuring the speed of sound in the material, may also be considered, but they present challenges in measuring dimensions. Overall, selecting the right instrument and method is crucial for achieving precise density measurements.