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 (ฯrยฒ), cylinders (ฯrยฒh), cones (โ ฯrยฒh), and spheres (โดโโฯrยณ) is critical for high school geometry.
๐ง Core Mental Strategies & Shortcuts
๐ฎ Sphere Volume Formula: V = โดโโ ฯ rยณ
For radius r = 3 cm: V = โดโโ ร ฯ ร 27 = 36ฯ cmยณ โ 113.1 cmยณ.
๐ฆ Cone is Exactly โ of a Cylinder: V = โ ฯ rยฒ h
A cone with base radius r and height h holds exactly one-third the volume of a cylinder with the same dimensions.
๐ฅซ Cylinder Volume Formula: V = ฯ rยฒ h
Multiply circular base area (ฯrยฒ) by the perpendicular height (h).
โ Frequently Asked Questions
Why do volume answers use cubic units (cmยณ, mยณ, inยณ)?
Volume measures 3 dimensions (length ร width ร height), so the units are multiplied together 3 times, creating cubic units.
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