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
- Volume calculations: Cube numbers help calculate volumes of cube-shaped objects
- 3D printing: Understanding cube numbers helps in designing 3D models
- Architecture: Building materials for cube-shaped structures
- Data science: Used in three-dimensional array calculations
- Gaming: Defining 3D environments and voxel-based games
Practice Problems
- What is the cube of 7?
- If the volume of a cube is 1,000 cubic meters, what is the length of one side?
- Find the difference between 5³ and 4³.
- 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.