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Volume - Monomath Math Dictionary
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V

Volume

Geometry

📖 Definition

Volume is the measure of the amount of three-dimensional space occupied by a solid object.

📝 Detailed Explanation

Volume is measured in cubic units such as cm³, m³, or in³. Different shapes have different volume formulas: cube (s³), rectangular prism (lwh), sphere (4πr³/3), cylinder (πr²h), cone (πr²h/3), and pyramid (Bh/3). Volume calculations are essential in physics (density = mass/volume), engineering, and construction.

📐 Formula

Sphere: V = 4πr³/3  |  Cylinder: V = πr²h

📜 History & Origins

Volume measurement dates to ancient civilizations for grain storage. Archimedes famously used water displacement to measure the volume of irregular objects (shouting "Eureka!"). He derived the volume of the sphere.

🔗 Related Terms

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