Cube | Formulas | Properties of Cube

Cube is a solid three-dimensional figure, which has 6 square faces or sides. Here we discuss here its Formulas, properties. Also, learn the surface area and volume formula for the cube. In real-life dices is a good example of the cube.

What is Cube?

A cube has six equal, square-shaped sides. Cubes also have eight vertices (corners) and twelve edges, all the same length. The angles in a cube are all right angles. A cube is a three-dimensional shape that features all right angles and height, width and depth that are all equal.

Cube

Part of Cube

Face:

A cube has six faces which are all squares, so each face has four equal sides and all four interior angles are right angles also called facets or sides. In the given figure, the 6 faces of the cube are:
ABCD, EFGH, ADHE, BCGF, ABFE and DCGH.

Edge:

The edge of the cuboid is a line segment between any two adjacent vertices. A cube has 12 edges. Because all faces are squares and congruent to each other, all 12 edges are the same length. In the given figure, the 12 edges of the cube are:
AB, BC, CD, DA, EF, FG, GH, HE, AE, DH, BF, CG.

Vertex:

A point formed where three edges meet is called vertex. A vertex is a corner. A cube has 8 vertices. In the given figure, the 8 vertices of the cube are:
A, B, C, D, E, F, G, H.

cube

Face Diagonals:

Face diagonals are line segments linking the opposite corners of a face. Each face has two, for a total of 12 in the cube. The length of the face diagonals is given by the formula

Length of Diagonal of Face of the Cube = √2 a

where a is the length of one side (edge). Since the faces are squares, this is the same as the diagonal of a square.

Space Diagonals:

Space diagonals are line segments linking the opposite corners of a cube, cutting through its interior. A cube has 4 space diagonals. The length of the space diagonal is given by the formula

Length of Diagonal of Cube = √3 a

Perimeter:

The perimeter of a cube found by adding all the sides. Cube has 12 sides.

Volume = 12 x side

Volume:

The volume of the cuboid is equal to the product of the area of one surface and height. Volume is measured in cubes (or cubic units)
For cube, length = breadth = height
Suppose length of an edge = a
Volume = length x width x height
Volume = a x a x a

Volume = a3

Surface Area:

For cube, length = breadth = height
Suppose length of an edge = a
Hence, surface area of the cube = 2(a × a + a × a + a × a) = 2 x 3a2

Surface Area = 6a2

Lateral surface

The sum of surface areas of all sides except the top and bottom face of solid is defined as the lateral surface area of a solid.

Lateral surface = 4× (side)2

Properties of Cube

• A cube has 6 square faces.
• A cube has 8 points (vertices).
• A cube has 12 edges.
• All faces of the cube are in a square shape.
• All the faces or sides have equal dimensions.
• The angles in a cube are all right angles
• The edges opposite to each other are parallel.

I hope, this article will help you a lot to understand the Cube | Formulas | Properties of Cube. If you still have any doubts and problems with any topic of mathematics you can ask your problem in the Ask Question section. You will get a reply shortly.

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