# Cube

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 Sub Topics A cube is a special type of a rectangular solid in which the length, width and height are exactly same. In geometry, a cube is a 3-dimensional solid, bounded by 8 vertices, 6 square faces, 12 sides, among which three meets at each vertex.

## Cube Definition

The definition of a cube states that it is a 3D, six sided solid figure with the same length, breadth, and height. The image given below explains what is a cube.

## Properties of a Cube

A cube is a 3 dimensional object that can be represented on a 2-dimensional surface by using the properties of a cube.

Listed below are some of the properties of a cube:
• All the faces of a cube are squares.
• All the faces meet four other faces.
• All the plane angles are right angles.
• All the vertices meet three faces.
• Opposite edges on faces of a cube are parallel to each other.
• Length of Face diagonal = $\sqrt{2}$ a units, where 'a' is the side of a cube.
• Length of Body diagonal or diagonal of cube = $\sqrt{3}$ a units, where 'a' is the side of a cube.

### Relation between Surface Area and Volume of a Cube:

Volume of a cube = a3 cubic units

Total surface area of a cube = 6a2 square units

Volume = ($\sqrt{\frac{Surface \ Area}{6}})^3$.

## Volume of a Cube

The amount of space occupied by the object is called as cube volume. The unit of measurement for volume of cube is m3, cm3, inches3 etc. The first step to solving problems related to cube is to read and understand what information the question holds. The volume of a cube formula is given as follows:

Volume of a Cube = Side * Side * Side = (Side)3

Given below are some of the examples that explains how to find the volume of a cube with the help of the formula for volume of a cube.

### Solved Example

Question: Find the volume of a cube with side 5 inches.
Solution:
Side of a cube = 5

Volume of a Cube = (Side)3

Volume of a Cube = (5)3

= 5 * 5 * 5

= 125

Therefore, the volume of a cube is 125 cubic inches.

## Surface Area of a Cube

The area of the surfaces of an object is called the surface area of the object. It's unit of measurement is m2, cm2, inches2 etc. The surface area of cube is the area on the outer side of a three-dimensional shape. Surface area formula for a cube helps us to find the length of the outer part of the solid. The formula for the surface area of a cube is given as follows:

Surface area of a Cube = 6 side2

Given below are some of the examples that explains how to find surface area of a cube with the help of the surface area of a cube formula.

### Solved Example

Question: Find the surface area of a cube with side 4 inches.
Solution:
Side of a cube = 4

Surface area of a cube = 6 side2

Surface area of a cube = 6 * 42

= 6 * 4 * 4

= 96

Surface area of a cube = 96 sq. inches.