Volume of Cube
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Volume of Cube

- Doubling the Cube Volume

Doubling the Cube Volume

A cube with an original side length (S1) of 5 units and corresponding volume (V1) of 125 cubic units has a new side length (S2) of 6.3 units when the volume is doubled (V2) to 250 cubic units.

*Answers rounded to three decimal places

Doubling the Cube Formula for Side

The cube doubling problems refers to doubling the volume of the cube. When the volume of the cube doubles at what rate does the side length increase? The formula below is used to calculate the side length of a doubled cube given an original cube with known side length:

  • S2 = S1 x ∛2

Substitute the formula for doubled side length in to the formula for cube volume to directly find the volume of a cube (V2) with twice the volume (V1) of the original cube.

  • V2 = (S1 x ∛2)3

What about finding the side length of the doubled cube if you only know the volume of the original cube? Recall the formula for finding the side length of the cube from the volume (S = ∛V) and substitute.

  • V2 = (∛V1 x ∛2)3

Although we can solve this problem via the use of modern computational techniques it is known as one of the great epic problems in mathematics. Using the classical mathematical tools, a compass and a straight edge, the number ∛2 could not be constructed, therefore the problem was rendered unsolvable. Read more about the challenges of doubling the cube.

Doubling of cube formula

Given an original cube with a side length S1 the side length S2 of a cube with twice the volume can be found by multiplying the original side length by ∛2.


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

Cube Face Diagonal
Cube Space Diagonal
Radius of Inscribed Sphere
All formulae...


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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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