Cube

In ancient times during the Old Babylonian period (20th to 16th centuries BC) mathematicians of Mesopotamian civilizations created cuneiform tablets for calculating cubes and cube roots A cube is a three-dimensional solid object which has 6 square faces, 8 vertices, and 12 edges. In other words, we can also say that it’s a regular hexahedron and the most common example of a cube that you see in daily life is a Rubik cube and dice. The other solid shapes like cubes are cuboid, cylinder, cone, sphere, etc.

Cube: Definition

A cube is a solid object which has 6 equal sides. length, breadth, and width all are equal if a length of a cube is 5 cm then the breadth and width of the cube is also 5 cm

Side of a cube – a

Here ‘a’ stands for the side of a cube.

Volume of a Cube

We can understand the volume of a cube formula by the following steps –

• Take any Paper square-shaped
• Now all the area covered by square sheet paper is known as the ‘ Surface area of the cube ‘ and as we know that all the sides of a  cube are equal so length, breadth, and width of the cube are equal so the surface of a cube is – “Side^3″
• A cube is made by stacking multiple square sheets on top of each other So height is ‘a’ unit
• So we can conclude the overall area of the cube by multiplying height with the area of bases

The volume of the cube = a² × a = a³

For example – By using the volume of cube formula find the volume of dice of side 10 cm

Side of a dice – 10 cm

The formula of volume of the cube – a³

By using the formula you can find that – 10cm ×10cm ×10cm = 1000 cm³

How to find cube roots?

Cube Root by Factorization Method– to find out the cube root first we have to make factors of a given digit and if the digit makes the perfect pairs of 3 then we can conclude that it is a perfect cub

For example – Assume the digit is 64

Now to find out its cube root first make the factors of 64

64= 2×2×2×2×2×2

= 4×4×4

4 make a perfect cube of 64. So, 4 is the cube root of 64

Properties of a cube

• All the sides of a cube are equal
• A cube has 6 square faces
• The vertices meet 3 faces and 3 edges
• The angles at a right angle

Difference between cube and cuboid

Cube

• A cube is a 3rd object
• All the edges of a cube are equal
• All the six faces in a cube make a square
• A cube has 12 diagonals and all sides are equal

Question– A cubicle size box has a height of 8 cm find its volume?

Solution –   Height of cube – 8cm

As all the sides of the cube are equal so the height of the cubical box equals its length and width also, the length and breadth of the cube are also 8cm.

Volume of the cube =a³

Here ‘a’ stands for the side of the cube

a = 8

Volume of cube = a³

=   (8)³

The volume of cube = 216

Cuboid

• A cuboid is also the 3rd object
• All the edges of a cuboid are not equal
• All the six faces in a cube make a square
• A cuboid has 12 diagonals and all sides of the diagonal are not equal

Question – A lunch box of height 10 cm, breadth 8cm, and length 6cm. Find the volume of the cuboid?

Solution – Height = 10 cm

Length = 6cm

Breadth = 8cm

Formula we used to find out volume of cuboid = L × B × H

= 6 cm × 8 cm × 10 cm

=   480 cm³

How Square is different from Cube?

Square is a 2-dimensional figure and its two dimensions are length and breadth whereas cube is a 3-dimensional figure and its three dimensions are its length, breadth, and width.

Square example–   Find the area of a square of side 7cm?

It is a square so both sides are equal so one side is 7 cm then another side is also 7 cm.

The formula we used to find out the area of square = length × breadth

As both sides of the square are equal

Area of square= 7 cm × 7cm

Area of square = 49cm²

Conclusion

To conclude, we can say that the formulas to calculate different measures of cubes, and cuboids have been in practice since ancient times. One must keep in mind the essential formulas to be able to calculate cube roots, sides, volumes of cubes and cuboids and other such hexahedrons accurately.