Calculate the exact volume and total surface area of any regular cube from its edge length. View real-time arithmetic breakdown and unit conversions.
A cube is a regular hexahedron with 6 equal square faces, 12 equal edges, and 8 vertices. Its volume is derived from length × width × height:
For a sphere inscribed inside this cube, the sphere's radius is \(r = \frac{a}{2}\). You can compare this with the Sphere Volume Formula to observe the volumetric difference between curved and orthogonal geometries.
The volume of a cube is V = a³, where 'a' is the length of any of the cube's equal edges.
A cube circumscribed around a sphere of radius r has side length a = 2r and volume V = (2r)³ = 8r³. A sphere inside this cube has volume V = (4/3)πr³ ≈ 4.189r³, occupying about 52.4% of the cube's volume.
A cube has 6 identical square faces, so its total surface area is A = 6a².
V = (4/3)πr³.V = πr²h.A = 6a².