# Cube formula - Volume and area

Cube formula – Area and volume formulas for your easy understanding.

Definition: Cube is a three dimensional object which has six equal square faces. It has equal width and height. You can find cube formulas from following basic mathematics.

Here is a nice Article on How to Learn Engineering Mathematics in efficient way Let, length of one edge of cube is a, ## Area of cube Formula

Area of a cube is defined as total number of square unit of cube surface area.

In other words, we can say six times of area of one face. Because cube has six equal square faces.

Area of cube formula A=6{ a }^{ 2 }

## Volume of cube Formula

Volume of cube is product of surface area by its height. Alternatively we can say, Cube volume is product of length, height and width of cube. Volume for cube formula can be formed by this relationship.

What is meant by volume is the cubic space occupied by a 3 dimensional object.

For a visual imagination say you have a cubic tank. It is each 1 meter in length, width and height. If you pour water into the tank completely, the amount of water occupied is the volume of cube.

Let’s derive formula for a cube (Volume),

1. Let a cube be width, height and length be “a”
2. Let’s cut the cube by one unit of length, height and width.
3. So you can get “a x a x a” of small cubes.
4. So the formula be,
Area of cube formula V=6{ a }^{ 3 }

## How to design a cube

You can design a cube using a paper or hard board, paper, pencil, scissor and gum. Following is a cube template used to build a cube which has edge length of “a”. 1. Draw above template in a hard board or paper. “a” is the width, height and length of edges of the cube.
2. Top most square, left and right squares have small projections to fix the board or paper with gum.
3. Drawn in dashes are the lines where it get folded.
4. Cut the shape and fold them to form a cube.
5. Fix the projections using gum and complete the cube.

## Properties of Cube

1. It has 12 edges where opposite edges are parallel to each other.
2. Each 3 pair of faces are parallel to each other.
3. It has 6 faces and all its faces are square in shape.
4. All the faces and sides are equal in dimensions.
5. The plane angles of the cube are the right angle.
6. Each of the faces meets the other four faces.
7. Each of the vertices meets the three faces and three edges.

## Examples

Example 1: A cube has edge length of 3 cm. What is the volume and area of cube?

Given, the length of sides of the cube is 3 cm.

From theory, Volume of a cube = (length of sides of the cube)3

Therefore, Volume, V = (3 cm)3

V = 27 cm3

From theory, Area of a cube = 6 × area of one face

Therefore, Volume, V = 6 × 3 × 3 cm2

V = 54 cm2

Example 2: What is the length of the edges of the cube, if its volume is equal to 8 cm3.

Given, Volume of the cube = 8 cm3.

Let the length of the edges is a.

We know, by the formula,

The volume of a cube = (length of edges of the cube)3

Substituting the value, we get,

8 = a3

a = 3√8

a = 2 cm

Therefore, the length of the cube is 2 cm.

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