Volume Calculator
Volume measures the amount of 3D space an object occupies. Common formulas: cube (s³), rectangular prism (lwh), sphere (4πr³/3), cylinder (πr²h), cone (πr²h/3). Volume is measured in cubic units (m³, ft³) or capacity units (L, gal).
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Tip: Volume scales as the cube of linear dimensions. Double all dimensions → 8× the volume. Half all dimensions → 1/8 the volume. This is why large animals need relatively thicker bones than small ones.
- 1Cube: V = s³
- 2Rectangular prism: V = l × w × h
- 3Sphere: V = (4/3)πr³
- 4Cylinder: V = πr²h
- 5Cone: V = (1/3)πr²h
| Shape | Formula | Example (r=3, h=5) |
|---|---|---|
| Cube | s³ | s=3: 27 units³ |
| Rectangular prism | l×w×h | 3×4×5 = 60 units³ |
| Sphere | (4/3)πr³ | 4/3×π×27 = 113.1 units³ |
| Cylinder | πr²h | π×9×5 = 141.4 units³ |
| Cone | (1/3)πr²h | (1/3)×π×9×5 = 47.1 units³ |
| Pyramid | (1/3)×base×h | (1/3)×9×5 = 15 units³ |
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Fun Fact
Archimedes discovered how to measure the volume of irregular objects by water displacement — and allegedly ran through the streets of Syracuse shouting 'Eureka!' (I have found it!) when the insight struck him in his bath (~250 BCE).
References
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