Cubic Numbers

You know that the word ‘cube’ is used in geometry.

A cube is a solid figure which has all its sides .

How many cubes of side 1 cm will make a cube of side 2 cm? 812416

How many cubes of side 1 cm will make a cube of side 3 cm ? 271896

Consider the numbers 1, 8, 27, ... These are called perfect cubes or cube numbers.

Can you say why they are named so?

Each of them is obtained when a number is multiplied by taking it threetwoone times.

We note that:

1 = 1 × 1 × 1 = 1312

8 = 2 × 2 × 2 = 2322

27 = 3 × 3 × 3 = 3332

We get: 53 = 5 × 5 × 5 =

Therefore, 125 is a cubesquare number.

Is 9 a cube number? NoYes

As 9 = × and there is no natural number which multiplied by taking three times gives 9.

We can see also that 2 × 2 × 2 = and 3 × 3 × 3 = .

This shows that 9 is not a perfect cube.

The following are the cubes of numbers from 1 to 10:

There are only ten perfect cubes from 1 to 1000. How many perfect cubes are there from 1 to 100? Observe the cubes of even numbers. Are they all even? What can you say about the cubes of odd numbers?

Fill the given below table to know the cubes of the numbers from 11 to 20.

Consider a few numbers having 1 as the one’s digit (or unit’s). Find the cube of each of them. What can you say about the one’s digit of the cube of a number having 1 as the one’s digit?

Similarly, explore the one’s digit of cubes of numbers ending in 2, 3, 4, ... , etc. Based on your observations, drop the given below numbers in the correct category:

Find the one’s digit of the cube of each of the following numbers

Instructions