Regular Tetrahedron Edge from Volume

Find the edge length of a regular tetrahedron from its volume, plus surface area, height, and circumscribed and inscribed sphere radii.

Input

Enter the volume of a regular tetrahedron to work back to its edge length.

Volume V

Edge length

a = 9.467212

Surface area

155.240414

Height

7.729946

Circumradius

5.797459

Inradius

1.932486

The length unit matches the cube root of the volume unit. Areas scale as length squared and volumes as length cubed.

The volume of a regular tetrahedron is V equals a cubed divided by 6 root 2. Solving for the edge a gives a equals the cube root of 6 root 2 times V.
The surface area is S equals root 3 times a squared, and the height is h equals the square root of two thirds times a.
The circumscribed sphere radius is R equals root 6 times a over 4, and the inscribed sphere radius is r equals root 6 times a over 12.
The length unit matches the cube root of the volume unit. For example, a volume in cubic centimeters yields an edge in centimeters.

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