Volume of Cube
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Volume of Cube

- Sphere Radius Tangent to Edge of Cube

Tangent Sphere Radius



A cube with a side length (S) of 5 has a tangent sphere with a radius (R) of 3.5355.

Tangent Sphere Radius Formula

for cubes with a side length S find the radius R of the sphere tangent to the cube edges

  • R = S/√2

substitute the side length S with the measured value, in this example lets use a side length of 5

  • R = 5/√2

divide the side length by the square root of 2 to find the radius of a sphere tangent to the edges of the cube

  • R = 3.5355
Radius of a Sphere Tangent to the edge of a Cube Formula

Given a cube with a side length S the radius (R) of a sphere tangent to the cube edges can be found by dividing the cube side length by the square root of two (2).

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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