The Volume of the Sphere

We already know how to find the volume of a cylinder and cone, so from these we can find the volume of a sphere.

Volume of cylinder of height 2r and radius r:  V_cylinder =  πr^{2 .} 2r = 2π r³

Volume of (single) cone of height r and radius r:  V_cone = 1/3 πr^{2 .} r = 1/3 πr³

Volume of cylinder hollowed out by a double cone:

V_{hollowcylinder} = 2π r³ – 2 ^. 1/3 πr³ = 6/3 πr³ – 2/3 2π r³ = 4/3π r³

The volume of the sphere is the same as the volume of the hollowed out cylinder:

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