Stated capacity is a brim measurement
Most vessels are described by how much they hold filled to the rim. Nobody brews to the rim: a gaiwan filled to the rim cannot be lidded and poured, a teapot filled to the rim spills through the lid hole, and leaf displaces volume as it expands. Usable capacity is commonly a fifth to a third less than the stated figure. Measure yours once with water and a scale — a gram of water is a millilitre — and use that number for every ratio afterwards. This single measurement resolves a great many complaints about a tea being stronger or weaker than the instructions predicted.
Volume and cooling are the same question
A small volume of water has a large surface relative to its mass, so it loses heat quickly; a large volume holds temperature far longer. This is why a 100 ml gaiwan can be filled with boiling water for a green tea that would be ruined by boiling water in a 700 ml pot: the small vessel has dropped several degrees before the leaf has properly wetted, and the large one has not. It is also why small-vessel brewing tolerates short steeps and large-vessel brewing does not. Capacity is a thermal variable before it is a serving variable.
Match capacity to how you drink, not to how you imagine drinking
A pot larger than one sitting produces tea that cools on the leaf and is drunk cold or thrown away. Most people drink less per sitting than they think and buy larger than they need. For one person, 200 to 350 ml covers a western steep; for gongfu, 100 to 150 ml is a full session vessel and anything larger is a serving pot. If you regularly make tea for four, buy for four and accept that the same pot will be wrong for you alone — one vessel cannot do both without one of the cases being bad.
Why a bigger pot is not a scaled-up small one
Doubling the vessel does not double the brew, because the surface-to-volume ratio, the heat loss and the depth of the leaf bed all change with size. That argument is set out in full in the guide on scaling a brew; the relevant conclusion here is that the ratio you learned in one vessel is a starting point in another, not a conversion.
The small exceptions
Aroma cups and tasting cups are deliberately small so one infusion fills one, and a larger cup makes a session look meagre. A serving pitcher should be slightly larger than the brewing vessel so a full infusion fits with room to swirl. A cooling bowl wants to be wide rather than large. And a kettle should be sized to how much you actually boil, because a kettle habitually filled to a quarter takes longer to heat proportionally and scales faster.