Volume of Cube

- Cube Circumscribed Sphere Volume

Circumscribed Sphere Volume

Side Length (S):

Sphere Volume (V):

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)πR³

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

Volume of a Sphere Circumscribing a Cube Formula

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.

Formulas

What is the formula for the volume of a Cube?

V = S³

What is the formula for the volume of a Rectangular Prism?

V = L x W x H

Other Formulae

for cubes with side length S

Cube Surface Area

6S²
Cube Face Diagonal: (√2)S
Cube Space Diagonal: (√3)S
Radius of Inscribed Sphere: S/2

All formulae...

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Definitions

Cube: A cube is a three dimensional geometry with six equal square faces meeting at ninety degrees along each edge and aligned with each vertex being formed from the intersection of three squares so that a completely enclosed volume is formed
Rectangular Prism: A rectangular prism is a three dimensional geometry with six faces. Unlike a cube the edge legths of each face may be unequal but parallel. Like a cube all faces must meet along the edges and align to form a vertex from the intersection of three faces so that the prism has a completely enclosed volume.

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