Cubes
Chapter Name : Cubes And Cube Roots |
Sub Topic Code : 104_08_07_02_03 |
Topic Name : Cubes |
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Sub Topic Name : Smallest Multiple That Is A Perfect Cube |
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Introduction
What is a perfect cube?
Pre-Requisites:
Basic knowledge about arithmetic operations, numbers, cubes
Activity:
The cube of a number is found by multiplying the number with itself twice. prime factorization can be used to find the cube roots of a number. Depending on the number of prime factors, the largest number to be divided or smallest number to be multiplied is found.
Real Life Question:
What is the capacity of your overhead tank?
Key Words / FlashCards
| Key Words | Definitions (pref. in our own words) |
|---|---|
| Cube number | A number when multiplied by its square number results in its cube number? |
Learning aids / Gadgets
| Gadgets | How it can be used |
|---|---|
| Abacus | Represent the prime factor to the left end of the abacus. Leave a row and represent the number. Divide until the prime factor can be no longer used. Now go to the next prime factor until the quotient becomes 1. Check the number of times the prime factor is repeated. |
Real life uses :
Volume estimation, height estimation in a cuboid, toys, electrical resistance, induction instruments
Practical examples around us
| Examples | Explainations |
|---|---|
| Overhead tanks | The volume of a tank is a cubic unit. For a cube tank, the volume will be the cube of the side. |
| Rubber band toys | The rubber band planes whose propeller is twisted first and rotates when left uses the cubic equations. |
What you learn in Theory:
The cube of a number is the product of the number with its square. The cube roots of a cube can be found by prime factorization and by sum of consecutive odd numbers. To make a number perfect cube, either it should be divided or multiplied depending on the number of times a prime factor is used.
What you learn in Practice:
The cube number is found by multiplying a number with the same number on the abacus two times. On first multiplication we obtain the square of the number. When the square of the number is multiplied by the number again, we obtain the cube number. Divide this number with the prime numbers until the quotient becomes 1. If quotient is 1 and the prime numbers are used in the multiples of 3, then the number is a perfect cube. If not, to make it a smallest perfect cube, the product of prime factors which are not in multiples of 3 divides the number. To make it largest perfect cube, the prime factors which are not in multiples of 3 are multiplied until they become in multiples of 3.