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Cylinder Geometry: Volume, Surface Area & Relation to Sphere

A cylinder has two parallel circular bases. Archimedes proved a sphere has exactly 2/3 the volume of its circumscribed cylinder.

Key Formulas for Cylinder
Volume: V = \pi r^2 h
Surface Area: A = 2\pi r h + 2\pi r^2

Archimedes' Cylinder and Sphere Connection

Archimedes considered his greatest mathematical achievement to be discovering that a sphere inscribed within a right circular cylinder has both a volume and a surface area equal to exactly two-thirds (2/3) that of the cylinder.

Formulas for Cylinder

Volume = π × r² × h
Surface Area = 2πrh + 2πr²

Calculate Cylinder Dimensions Instantly

Need to calculate volumes, areas, or radius values quickly? Use our interactive math calculators:

Sphere Volume Calculator Hemisphere Calculator

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