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Why can we measure the volume of a liquid directly, but not a solid?  

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Matter has 3 main states or forms: solid, liquid and gas (plasma is another form of matter, but it is not commonly observed). Solids, liquids and gases are classified based on their intermolecular attraction. Solids have the highest intermolecular attraction among all the states of matter. This is the reason solids are so compact and rigid. Liquids have less intermolecular attraction as compared to solids. They find it easier to flow and occupy the shape of the container they are in. Gases have the least intermolecular attraction (when compared to other forms of matter).

The ability to flow makes the volumetric measurement of liquids easy. If we need to measure the volume of a given liquid, we can transfer it to a measuring cup or cylinder or beaker and calculate its volume using the graduations on the vessel. In comparison, solids cannot flow and hence cannot be transferred to measuring vessels (beaker, cup, etc.). To determine the volume of a solid, we have to measure its dimensions and use geometry to calculate its volume. We could also submerge the solid into a known amount of water and measure the volume of water that it displaces.

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