Volume
Volume is the amount of space an object or liquid occupies, measured in milliliters or cubic centimeters using a formula or water displacement.
Formula
V = l \times w \times h
Definition
Volume is how much space something takes up: for a liquid you read it off a measuring container, and for a box shape you multiply length times width times height, $V = l \times w \times h$. It is measured in liters and milliliters for liquids or cubic centimeters and cubic meters for solids, with $1\ \text{mL} = 1\ \text{cm}^3$, and an irregular solid's volume is found by water displacement: submerge it in a graduated cylinder and subtract the starting level from the final level. Volume is an extensive property that scales with the amount of material and, for liquids and gases, depends on temperature and pressure. Displacement is valid only for objects that sink and neither absorb nor dissolve in the liquid, and the cylinder's graduations usually set the limiting uncertainty in a density measurement.
Example
A block $4\ \text{cm}$ long, $2\ \text{cm}$ wide, and $3\ \text{cm}$ tall has a volume of $4 \times 2 \times 3 = 24\ \text{cm}^3$, and water poured to the $50$ line in a cylinder has a volume of $50\ \text{mL}$. A cylinder holds $20.0\ \text{mL}$ of water, a rock is lowered in, and the level rises to $25.0\ \text{mL}$, so the rock's volume is $5.0\ \text{cm}^3$ and with a mass of $13.5\ \text{g}$ its density is $2.7\ \text{g/cm}^3$. That $5.0\ \text{mL}$ from a cylinder graduated every $1\ \text{mL}$ carries roughly $\pm 0.14\ \text{mL}$ in the difference of two readings, near $3\%$, and a $10\ \text{mL}$ cylinder graduated every $0.1\ \text{mL}$ would cut that about tenfold, more than any better balance could.
Key Insight
One milliliter and one cubic centimeter are the same amount of space; a sugar cube is about $1\ \text{cm}^3$ and would hold about $1\ \text{mL}$ of water if hollow. Displacement works because two things cannot occupy the same space, so the water that moves out of the way has exactly the volume of the object that moved in. Volume is the measurement most sensitive to technique, and a trapped air bubble, a wet cylinder wall, or a meniscus read from above each bias it in a known direction, so knowing which way each error pushes lets you diagnose an off density before repeating the trial.