## Circumscribed Sphere Volume

A cube with a side length (S) of 2 has a circumscribed sphere with a volume (V) of 21.7656.

## Circumscribed Sphere Volume Formula

the Volume of a sphere with radius (R) can be found with this formula

- V = (4/3)πR
^{3}

the radius (R) of a sphere that circumscribes a cube with side length S:

- R = S * √3/2

by combining the two formulae we can determine the Volume of a circumscribed sphere in terms of cube Side length

**V = (4/3)π(S * √3/2)**^{3}

Given a cube with a side length S the volume (V) of a circumscribed sphere can be found by substituting the formula for finding the Radius of a circumscribed sphere into the formula for finding the Volume of a sphere.