## Tangent Sphere Volume

A cube with a side length (S) of 5 has a sphere tangent to its edges with a volume (V) of 185.1201.

## Tangent 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 tangent to the edges of a cube with side length S can be determined

- R = S/√2

the Volume of a sphere tangent to the edge of a cube in terms of cube Side length

**V = (4/3)π(S/√2)**^{3}

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