Cube Numbers 1-20: Simple Explanations & Examples for Students


What is a Cube Number?

A cube number (or "perfect cube") is what we get when we multiply a number by itself three times. It's like building a cube with equal sides!

Mathematically, we write this as:

  • n³ = n × n × n (where n is any number)

Cube numbers are called "cube" because they represent the volume of a cube with sides of length n.

Cube Numbers from 1 to 20

Let's explore cube numbers for integers 1 through 20:

1 cubed (1³)

1³ = 1 × 1 × 1 = 1

  • Example: A cube with sides of 1 unit has a volume of 1 cubic unit.

2 cubed (2³)

2³ = 2 × 2 × 2 = 8

  • Example: A sugar cube with sides of 2 cm has a volume of 8 cubic cm.

3 cubed (3³)

3³ = 3 × 3 × 3 = 27

  • Example: A Rubik's cube (3×3×3) has 27 smaller cubes making it up.

4 cubed (4³)

4³ = 4 × 4 × 4 = 64

  • Example: A cube-shaped box with sides of 4 inches has a volume of 64 cubic inches.

5 cubed (5³)

5³ = 5 × 5 × 5 = 125

  • Example: A cube-shaped aquarium with 5-foot sides holds 125 cubic feet of water.

6 cubed (6³)

6³ = 6 × 6 × 6 = 216

  • Example: A cube-shaped room with 6-meter sides has a volume of 216 cubic meters.

7 cubed (7³)

7³ = 7 × 7 × 7 = 343

  • Example: A cube made of 7×7×7 smaller cubes contains 343 smaller cubes in total.

8 cubed (8³)

8³ = 8 × 8 × 8 = 512

  • Example: A digital cube in a game made of 8×8×8 blocks contains 512 blocks.

9 cubed (9³)

9³ = 9 × 9 × 9 = 729

  • Example: A cube-shaped warehouse with sides of 9 yards has a volume of 729 cubic yards.

10 cubed (10³)

10³ = 10 × 10 × 10 = 1,000

  • Example: A kiloliter (1,000 liters) can fill a cube with sides of 10 decimeters.

11 cubed (11³)

11³ = 11 × 11 × 11 = 1,331

  • Example: A cube with sides of 11 units contains 1,331 unit cubes.

12 cubed (12³)

12³ = 12 × 12 × 12 = 1,728

  • Example: A cubic foot contains 1,728 cubic inches (12×12×12).

13 cubed (13³)

13³ = 13 × 13 × 13 = 2,197

  • Example: A cube-shaped container with sides of 13 cm holds 2,197 cubic cm.

14 cubed (14³)

14³ = 14 × 14 × 14 = 2,744

  • Example: A cube-shaped storage unit with sides of 14 feet has a volume of 2,744 cubic feet.

15 cubed (15³)

15³ = 15 × 15 × 15 = 3,375

  • Example: A 15×15×15 Minecraft cube contains 3,375 blocks.

16 cubed (16³)

16³ = 16 × 16 × 16 = 4,096

  • Example: A cube formed by 16×16×16 smaller cubes has 4,096 total cubes.

17 cubed (17³)

17³ = 17 × 17 × 17 = 4,913

  • Example: A cube with sides of 17 meters has a volume of 4,913 cubic meters.

18 cubed (18³)

18³ = 18 × 18 × 18 = 5,832

  • Example: An 18×18×18 grid in a 3D modeling program creates 5,832 intersection points.

19 cubed (19³)

19³ = 19 × 19 × 19 = 6,859

  • Example: A cube-shaped sand pile with sides of 19 feet contains 6,859 cubic feet of sand.

20 cubed (20³)

20³ = 20 × 20 × 20 = 8,000

  • Example: A cube with sides of 20 cm has a volume of 8,000 cubic cm, which equals 8 liters.

Visual Understanding of Cube Numbers

Imagine building cubes with small blocks:

  • 1³: Just 1 single block
  • 2³: A cube with 2 blocks on each side (8 total)
  • 3³: A cube with 3 blocks on each side (27 total)

This pattern continues as cube numbers grow!

Interesting Patterns in Cube Numbers

The Difference Between Consecutive Cubes

The difference between consecutive cube numbers follows a pattern:

  • 8 - 1 = 7
  • 27 - 8 = 19
  • 64 - 27 = 37
  • 125 - 64 = 61
  • 216 - 125 = 91

Notice how these differences increase by 12, 18, 24, 30... (adding 6 each time)

Sum of Cubes Formula

The sum of the first n cube numbers equals the square of the sum of the first n numbers!

For example, for n = 4: 1³ + 2³ + 3³ + 4³ = 1 + 8 + 27 + 64 = 100 (1 + 2 + 3 + 4)² = 10² = 100

This works for any value of n!

Real-Life Applications of Cube Numbers

  1. Volume calculations: Cube numbers help calculate volumes of cube-shaped objects
  2. 3D printing: Understanding cube numbers helps in designing 3D models
  3. Architecture: Building materials for cube-shaped structures
  4. Data science: Used in three-dimensional array calculations
  5. Gaming: Defining 3D environments and voxel-based games

Practice Problems

  1. What is the cube of 7?
  2. If the volume of a cube is 1,000 cubic meters, what is the length of one side?
  3. Find the difference between 5³ and 4³.
  4. If you build a cube with 3×3×3 smaller cubes, how many cubes are visible from the outside?

Conclusion

Cube numbers represent the volume of cubes and have many applications in mathematics and real life. Remember, to find a cube number, simply multiply the number by itself three times (n×n×n). The cube numbers from 1 to 20 form a foundation for understanding higher-level mathematical concepts and spatial reasoning.

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