3D Geometry Volume Formulas: Sphere, Cone, Cylinder, Prism
Volume measures the 3-dimensional space (capacity) enclosed by a solid shape. Mastering the foundational relationship between circles (πr²), cylinders (πr²h), cones (⅓πr²h), and spheres (⁴⁄₃πr³) is critical for high school geometry.
🧠 Core Mental Strategies & Shortcuts
🔮 Sphere Volume Formula: V = ⁴⁄₃ π r³
For radius r = 3 cm: V = ⁴⁄₃ × π × 27 = 36π cm³ ≈ 113.1 cm³.
🍦 Cone is Exactly ⅓ of a Cylinder: V = ⅓ π r² h
A cone with base radius r and height h holds exactly one-third the volume of a cylinder with the same dimensions.
🥫 Cylinder Volume Formula: V = π r² h
Multiply circular base area (πr²) by the perpendicular height (h).
❓ Frequently Asked Questions
Why do volume answers use cubic units (cm³, m³, in³)?
Volume measures 3 dimensions (length × width × height), so the units are multiplied together 3 times, creating cubic units.
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