How to Find the Surface Area and Volume of a Cube?

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surface area of cube

A solid three-dimensional figure that has 6 faces in the shape of a square, 8 vertices, and 12 edges is known as a cube. In other words, a cube is a block where the measure of height, breadth, and length are equal. Concepts such as volume and surface area of cube are computations performed on a cube. The 8 vertices and 12 edges are placed in such a way that 3 edges meet at one vertex. A common daily use object in the form of a cube is a Rubik’s cube. A cube is also known as a regular hexahedron, right rhombohedron, square parallelepiped, and an equilateral cuboid. Additionally, it is also a trigonal trapezohedron in four orientations and a regular square prism in three orientations.

Surface Area

There are two types of surface areas used while dealing with a cube, namely – lateral surface area (LSA) and total surface area (TSA). Let us take a detailed look at both concepts.

Lateral Surface Area

The LSA is defined as the area occupied by the walls, excluding the top and bottom. As there is no curved surface hence, we do not calculate the curved surface area. For the LSA, as the sides of the cube are in the form of a square; thus, we have to calculate the area of each square and then multiply it by 4 to get the area of the cube. We do not consider the base and the top in the formula.

LSA = 4 * area of square = 4 * side2

Total Surface Area

The TSA is defined as the total area that is occupied by the entire cube in a plane. The TSA is given by the sum of the LSA, the base, and the top. Suppose the side of a cube measures p. Then we get the TSA by the following steps.

1. Area of a square = p2

2. LSA of the cube = 4p2

3. TSA of the cube = LSA + area of base + area of top = 4p2 + p2 + p2 = 6p2.

Volume of a Cube

The volume of the cube is defined as the capacity or the space contained within the cube. It is expressed as the product of height, breadth, and length. As all these dimensions are of the same measure, we can denote them by p. The volume of cube formula is given as follows:

Volume = length * breadth * height = p * p * p = p3

Diagonals of a Cube

The diagonal is a line segment joining one vertex to the opposite vertex. A cube has two types of diagonals, one that lies on the face and one that lies within the cube.

1. Face diagonal length = √2 * side.

2. Cube’s diagonal length = √3 * side

Properties of a Cube

1. The faces of a cube are all in the shape of a square.

2. As all faces are in the shape of a square, they have equal dimensions.

3. A cube’s plane angles measure 90 degrees.

4. Each vertice of a cube meets the three edges as well as three faces.

5. The edges that are opposite to each other are parallel and equal in measure.

Conclusion

A cube is the most basic figure that kids are introduced to when studying surface areas and volumes. The figures get more complicated after that; hence, kids should turn to an online educational platform such as Cuemath to build a strong mathematical foundation. At Cuemath, kids can master a subject in no time and have an enjoyable experience.