What is a Cube?

S3-SA2-0124

Grade Level:

Class 7

AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering

Definition

What is it?

A cube of a number is simply that number multiplied by itself three times. For example, the cube of 2 is 2 x 2 x 2. It helps us understand how numbers grow very quickly.

Simple Example

Quick Example

Imagine you have a magic box that doubles your money. If you put in 5 rupees, it gives you 5 x 5 x 5 rupees. So, the cube of 5 is 125. You'd get 125 rupees!

Worked Example

Step-by-Step

Let's find the cube of the number 4.
---Step 1: Understand what 'cube' means. It means multiplying the number by itself three times.
---Step 2: Write down the number: 4.
---Step 3: Multiply the number by itself once: 4 x 4 = 16.
---Step 4: Now, multiply that result (16) by the original number again: 16 x 4 = 64.
---Step 5: So, the cube of 4 is 64.
Answer: 64

Why It Matters

Understanding cubes is crucial in fields like Computer Science for calculating memory storage or in Physics to understand volumes of 3D objects. Engineers use it to design strong structures, and Data Scientists might use it in complex calculations for predictions. It opens doors to many exciting careers!

Common Mistakes

MISTAKE: Thinking the cube of a number means multiplying it by 3 (e.g., 5 x 3 = 15 for the cube of 5) | CORRECTION: The cube means multiplying the number by ITSELF three times (e.g., 5 x 5 x 5 = 125).

MISTAKE: Confusing cube with square (e.g., calculating 3 x 3 = 9 for the cube of 3) | CORRECTION: A square is multiplying by itself twice (x * x), while a cube is multiplying by itself three times (x * x * x). So, the cube of 3 is 3 x 3 x 3 = 27.

MISTAKE: Forgetting to multiply the intermediate result by the original number again (e.g., for cube of 2, doing 2 x 2 = 4 and stopping) | CORRECTION: Remember it's three multiplications. So, for cube of 2, it's 2 x 2 = 4, THEN 4 x 2 = 8.

Practice Questions

Try It Yourself

QUESTION: What is the cube of 6? | ANSWER: 216

QUESTION: A small tiffin box has a side of 3 cm. If its volume is the cube of its side, what is its volume? | ANSWER: 27 cubic cm

QUESTION: If the cube of a number is 1000, what is the number itself? (Hint: Think about which number multiplied by itself three times gives 1000) | ANSWER: 10

MCQ

Quick Quiz

What is the cube of 7?

343

777

The Correct Answer Is:

The cube of 7 means 7 multiplied by itself three times: 7 x 7 x 7. First, 7 x 7 = 49. Then, 49 x 7 = 343. Options A and B are incorrect as they represent 7x3 and 7x7 respectively.

Real World Connection

In the Real World

Imagine you're designing a new storage box for your school supplies. If the box has equal length, width, and height, its volume (how much it can hold) is calculated by cubing the length of one side. This is crucial for architects designing buildings or for ISRO engineers calculating fuel tank volumes for rockets!

Key Vocabulary

Key Terms

CUBE: A number multiplied by itself three times | EXPONENT: A small number written above and to the right of the base number, showing how many times the base number is to be multiplied by itself (e.g., 2^3, where 3 is the exponent) | VOLUME: The amount of space a 3D object occupies | BASE NUMBER: The number that is being multiplied by itself (e.g., in 5^3, 5 is the base number)

What's Next

What to Learn Next

Great job understanding cubes! Next, you should explore 'Cube Roots'. Cube roots are the opposite of cubes, helping you find the original number when you know its cube. It's like unwrapping the magic box!