Volume measures how much space an object occupies. Common units: cubic meters (m³), liters (L), cubic feet (ft³), gallons.
Common Formulas
- Cube: V = s³
- Rectangular prism: V = l × w × h
- Cylinder: V = πr²h
- Sphere: V = (4/3)πr³
- Cone: V = (1/3)πr²h
Conversions
1 m³ = 1,000 liters. 1 gallon (US) = 3.785 liters. 1 cubic foot = 7.481 gallons.
Volume vs. Capacity
Volume measures the space an object occupies (relevant for solids); capacity measures how much a container can hold (relevant for liquids and gases). They use compatible units — 1 liter of capacity occupies exactly 1,000 cm³ of volume — which is why the two concepts are often used interchangeably in everyday contexts.
Displacement Method
For irregularly shaped objects where no formula applies, volume can be measured by submerging the object in a graduated container of water and measuring how much the water level rises — the classic method famously attributed to Archimedes for testing a crown's purity.