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The shape of a cube is considered as “cubic”. We can also say that a cube is considered as a block, where all the length, breadth and height are the same. Along with that, it has 8 vertices and 12 edges such that 3 edges meet at one vertex point. Check the given image below, defining its faces, edges and vertices. It is also known as a square parallelepiped, an equilateral cuboid and a right rhombohedron. The cube is one of the platonic solids and it is considered as the convex polyhedron where all the faces are square. We can say that the cube has octahedral or cubical symmetry. A cube is the special case of the square prism.
Surface Area and Volume Formula For Cube
The surface area and the volume of the cube are discussed below:
Surface Area of a Cube
We know that for any shape, the area is defined as the region occupied by it in a plane. A cube is a three-dimensional object, therefore, the area occupied by it will be in a 3d plane. Since a cube has six faces, therefore, we need to calculate the surface area of the cube, covered by each face. The formula to find the surface area can be found as given below.
Let a be the edge of the cube.
Area of one face = Area of a square = a2
We know that the cube has 6 square shaped faces.
Lateral surface area (excluding the top and bottom faces) = 4 × Area of one face
LSA = 4a2
Total surface area = LSA + Area of the top and bottom faces
TSA = 4a2 + a2 + a2
TSA = 6a2
Volume of Cube
The volume of cube is the space contained in it. Suppose, if an object is in cubical shape and we need to immerse any material in it, say water, then the measure of water in litres to be kept in the object is calculated by its volume. The formula of the volume is given by:
Properties of Cube
The following are the important properties of cube:
- It has all its faces in a square shape.
- All the faces or sides have equal dimensions.
- The plane angles of the cube are the right angle.
- Each of the faces meets the other four faces.
- Each of the vertices meets the three faces and three edges.
- The edges opposite to each other are parallel.
Difference Between Square and Cube
The major difference between the square and the cube is the square is a two-dimensional figure and it has only two dimensions such as length and breadth, whereas the cube is a three-dimensional figure and its three dimensions are length, breadth and height. The cube is obtained from the shape square.