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Surface area of cube

Surface Area of Cube - Total surface area of cube, Lateral surface area of cube, Length of an edge and Length of a cube

A cube is a 3- dimensional shape. It has 6 faces, 8 vertices and 12 edges. Each vertex of a cube is the meeting point of 3 of its edges. The cube shape is also referred to as a cubic figure. All the sides or faces of a cube are equal. This is because a cube has its faces made up of squares which give cube equal sides.

Surface area of cube

The area occupied by a cube in three- dimensional space is called its surface area. The surface area of a cube is calculated as the product of 6 and square of length of it sides. It can also be calculated by adding the squares of length of all six sides of the cube. Since a cube is made of square faces, the area of cube can also be observed as the sum of areas of the six squares which make the cube. For example,

image

If we open up the cube in form of the constituent netted figures, then we will get six square figures. This makes finding the surface area of a cube very easy.

Thus, the above figure is of a cube with all sides equal. The area of given cube is calculated as

Surface area of cube = 6 . a²

Or

Surface area of cube = a² + a² + a² + a²2 + a² + a²

where ‘a’ is the length of sides.

The area is measured in square units.

However, the area of cube is of two types depending on the number of faces involved or required under given conditions. The types of areas of cube are as follows:

  1. Surface area or total surface area of cube (TSA)
    The total surface area or TSA of a cube refers to the area of all six faces of the cube. It involves the top and base as well.
    TSA or SA of cube = 6 . a²
  2. Lateral surface area of cube(LSA)
    The lateral surface area of a cube includes only four sides or faces of the cube. Generally, the lateral surface area of a cube involves the side faces but not the top and base of the cube. Therefore, the lateral surface area reduces to the sum of 4 square faces of a cube.
    LSA of a cube = TSA – 2a²
    LSA of a cube = 6a² – 2a²
    LSA of a cube = 4 . a²

Length of an edge of a cube

The edge of a cube is the line segment that joins two vertices of a single unit cube. The length of the edge of a cube can be calculated with the help of the surface area of the cube.

We know

Area of cube = 6a²

where ‘a’ is the side of the cube. This means ‘a’ is the edge of the cube. To find the length of ‘a’

a = √(area/6)

Length of a cube when the volume is given

The volume of the cube is given by a³

Thus, the side of the cube can be found out by calculating the cube root of the volume.

a= ∛a³

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