Cube
A cube is a three-dimensional solid object bounded by six equal square faces. It is one of the five Platonic solids.
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)
dface = a√2
Face diagonal (diagonal of one face)
Dspace = 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: dface = 5√2 ≈ 7.071 cm
Space diagonal: Dspace = 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.