Cube

A cube is a three-dimensional solid object bounded by six equal square faces. It is one of the five Platonic solids.

a a a

Properties

A cube has 6 faces, 12 edges, and 8 vertices. All edges are equal in length. The cube is a special case of a rectangular prism where length = width = height.

Basic Formulas

V = a³ Volume (edge cubed)
A = 6a² Surface area (six square faces)
d_face = a√2 Face diagonal (diagonal of one face)
D_space = a√3 Space diagonal (from one vertex to the opposite vertex through the interior)

Example

Given: edge a = 5 cm

Volume: V = 5³ = 125 cm³

Surface area: A = 6 · 5² = 6 · 25 = 150 cm²

Face diagonal: d_face = 5√2 ≈ 7.071 cm

Space diagonal: D_space = 5√3 ≈ 8.660 cm

Notes

The cube is one of the five Platonic solids (regular polyhedra). It is also a square prism. The space diagonal connects two opposite vertices and passes through the center of the cube.

The cube has the largest volume among all rectangular boxes with a given surface area.

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