Volume কী?

Example 38.3 (Volumes to know by heart)

A teaspoon holds about $5\,\mathrm{mL}$; a drinking glass about $25\,\mathrm{cL}$, a quarter litre; the milk carton, $1\,\mathrm{L}$; a bathtub, around $150\,\mathrm{L}$; a sugar cube takes about $3\,\mathrm{cm}^{3}$; a die about $4\,\mathrm{cm}^{3}$. Anchors like these make the judging step of every measurement possible.

Example 38.7 (The crown in the bathtub)

The old story: a king suspected his goldsmith had thinned the royal crown’s gold with silver, and asked the scientist Archimedes to find out without harming the crown. Stepping into a full bath, Archimedes watched the water slosh over the rim — and saw in a flash that the overflow measured his own body’s volume, lumps and all. Legend says he ran through the streets shouting “Eureka!” — I have found it! How the crown’s volume unmasked the fraud needs one more idea, two chapters ahead; the bathtub gave him the volume of anything.

Example 38.8 (Same volume, different mass)

Fill two identical $25\,\mathrm{cL}$ glasses, one with water, one with honey, and weigh them (subtracting the glasses): the honey glass holds noticeably more grams in the very same room. Same volume, different mass. And a litre of air weighs hardly more than a gram, in the room where a litre of water weighs a full kilogram. Room and stuff are truly different bookkeepers — hold that thought firmly: it becomes a law, with a name, in the last chapter of this year.