Volume of a Sphere

A sphere is the set of all points lying at a fixed distance from a centre. That distance is the radius, and it alone fixes the volume.

• $V$ — the volume
• $r$ — the radius
• $\pi$ — pi

Example

With the default radius $r = 5$, and since $5^3 = 125$,

The volume is about 523.5988.

The link with cylinders and cones

Sit a sphere of radius $r$ snugly inside a cylinder of base radius $r$ and height $2r$. The cylinder holds $\pi r^2 \times 2r = 2\pi r^3$, and the sphere fills exactly two thirds of it. A cone on the same base with the same height holds $\dfrac{2}{3}\pi r^3$, so cone, sphere and cylinder stand in the ratio $1 : 2 : 3$ — a relationship discovered by Archimedes.

Watch out

Only the radius is cubed. Writing $r^2$ in place of $r^3$ turns the expression into something close to the surface area formula, which is $4 \pi r^2$. Doubling the radius multiplies the volume by eight. If you know the diameter, halve it to get the radius before entering it.