Cube - Definition, Formula, Volume, Surface Area of Cube

Cube is one of the most commonly known three-dimensional figures to humankind. The dice we roll to play our favorite games like ludo, and snake & ladders is a cube. The famous Rubik’s cube is the best example of a cubic structure. It contains 27 smaller cubes with six different colors, and learning to solve it helps improve our cognitive functions. It enhances our cerebrum's thinking capacity. In simple terms, a cube is a 3D square. When drawn on a cartesian plane, a cube has a value of its x- axis, y-axis, and z-axis as equal. This means that all the sides or dimensions of a square are identical to each other. The main distinction between the square and the cube is that the square is a two- dimensional figure with just two dimensions (length and width), whereas the cube is a three- dimensional shape with three dimensions which includes length, breadth, and height along the x, y, and z-axis. Cube is a special type of prism known as a square prism. Some important characteristics of a cube to be remembered are:

• A cube contains six faces (surfaces having an area), and all the faces are square. The same measurements apply to all faces or sides. Every single face touches the other four faces and doesn’t connect with the exact opposite one.
• A cube extends 90 degrees on all its planes.
• A total of 12 edges are formed by a cube. Four on both the top and bottom plane and four in between them. The edges on the opposite sides are parallel to each other.
• Each vertex of the cube is connected to three edges and eventually three faces of the cube. There are a total of 8 vertices in every cube.

These were all the details about the shape and size of the cube. Let us now learn about some essential parameters like the surface area and the volume of a cube.

Surface Area

The surface area of a cube is the region of space that the cube covers in the 3D cartesian plane. We have already studied that there are six faces of a cube; hence the surface area of each face will constitute to make up the total surface area or TSA of a cube. Let us assume that the side of a cube is ‘s’. Area of a single face (square-shaped) = s 2 . Area of 6 faces = 6 x area of one face = 6 x s 2 = 6s 2 . This is termed the total surface area of a cube. The lateral Surface area or LSA of a cube is defined as the area contained by the entire cube except for the roof and floor of the cube. Without the top and bottom, there are four faces in a cube. Hence, LSA = 4 x side 2 = 4s 2

Volume

The volume of a cube can be defined as the amount of space or air contained inside the cube. It is calculated using the formula: The volume of a cube = s 3 . It is in cubic units (m or cm)

Diagonals

The line extending from one vertex of the cube to another is known as the diagonal of the cube. There are two types of diagonals present in a cube. First is the diagonal present only on the face of the cube. This diagonal goes from one vertex to another in a face. It is calculated by using the formula: (√2s). The second diagonal connects one vertex of the cube to another vertex and travels within the cube. The formula for this diagonal is (√3s).