Cubes 1 to 20 as the name suggests are the cubes of the natural number from 1 to 20. We calculate the cube of a number by multiplying the number by itself twice. Suppose we have to find the cube of a then it is found by multiplying a by itself two times as a × a × a. A cube is represented by taking 3 in the exponent of the given number. Suppose we have to find the cube of 11 then it is represented as 113 and is calculated as,
113 = 11 × 11 × 11 = 1331
Similarly, cubes 1 to 20, i.e. cubes of the numbers from 1 to 20 are found. In this article, we will learn about the cubes of numbers from 1 to 20, their charts, examples, and others in detail.
Cube 1 to 20
The cubes 1 to 20 are the cubes of the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20. These cubes are very useful in solving various mathematical problems and finding various patterns of numbers. Learning these cubes is essential for students to perform better in their classes.
The basics of cubes 1 to 20 are,
- Exponent Form: (x)3
- Lowest Value: 13 = 1 × 1 × 1 = 1
- Highest Value: 203 = 20 × 20 × 20 = 8000
What are Cubes 1 to 20?
Cubes 1 to 20 are very useful for the students to learn which helps them to solve various mathematical problems. We write the cube of any number as 13 = 1 and is read as 1 cubed equals 1, similarly, the other cube is read as 2 cubed equals 8, 3 cubed equal 27, and so on. The chart of the cubes from 1 to 20 is added below,
Cubes 1 to 20 List
Cube 1 to 20 list is a list containing the cubes of numbers from 1 to 20. The table added below contains all the cubes from 1 to 20. Now let’s learn these,
|
1
|
1
|
11
|
1331
|
|
2
|
8
|
12
|
1728
|
|
3
|
27
|
13
|
2197
|
|
4
|
64
|
14
|
2744
|
|
5
|
125
|
15
|
3375
|
|
6
|
216
|
16
|
4096
|
|
7
|
343
|
17
|
4913
|
|
8
|
512
|
18
|
5832
|
|
9
|
729
|
19
|
6589
|
|
10
|
1000
|
20
|
8000
|
Cubes 1 to 20 (Even Numbers)
Cubes 1 to 20 even numbers contain all the cubes of the even number from 1 to 20, i.e. it contains the cube of 2, 4, 6, 8, 10, 12, 14, 16, 18, and 20. The table added below shows the cube of all the even numbers from 1 to 20.
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(2)3
|
8
|
|
(4)3
|
64
|
|
(6)3
|
216
|
|
(8)3
|
512
|
|
(10)3
|
1000
|
|
(12)3
|
1728
|
|
(14)3
|
2744
|
|
(16)3
|
4096
|
|
(18)3
|
5832
|
|
(20)3
|
8000
|
Cubes 1 to 20 (Odd Numbers)
Cubes 1 to 20 odd numbers contains all the cubes of the odd number from 1 to 20, i.e. it contains the cube of 1, 3, 5, 7, 9, 11, 13, 15, 17, and 19. The table added below shows the cube of all the odd numbers from 1 to 20.
|
(1)3
|
1
|
|
(3)3
|
27
|
|
(5)3
|
125
|
|
(7)3
|
343
|
|
(9)3
|
729
|
|
(11)3
|
1331
|
|
(13)3
|
2197
|
|
(15)3
|
3375
|
|
(17)3
|
4913
|
|
(19)3
|
6859
|
How to Calculate Cubes 1 to 20?
Cubes from 1 to 20 are the cubes of the number from 1 to 20 and they are calculated by mostly two methods that are,
- By Multiplying the Number by Itself
- By Using Algebraic Identities
By Multiplying the Number by Itself
Cubes from 1 to 20 can be easily calculated by multiplying the number by itself two times i.e. suppose we have to find the cube of 9 then it is calculated as,
93 = 9 × 9 × 9 = 729
Thus, the cubes of all the numbers from 1 to 20 are calculated.
Using Algebraic Identities
Using algebraic identities one can easily find the cube of the number from 1 to 20. Suppose we have to find the cube of 9 and then using Algebraic Identities it is calculated as,
93 = (10-1)3
Using Algebraic Identity, (a – b)3 = a3 – b3 – 3ab(a – b)
⇒ 93 = (10)3 – (1)3 – 3(10)(1)(10-1)
⇒ 93 = 1000 – 1 – 270
⇒ 93 = 729
Thus, the cubes of all the numbers from 1 to 20 are calculated.
Solved Examples on Cube 1 to 20
Problem 1: Find the volume of a cubical tank whose side is 11 cm.
Solution:
Given,
Side of the cubical tank (a) = 11 cm
Volume of Cubical tank = a3 = 113 = 1331
Thus, the volume of cubical tank is 1331 cm3
Problem 2: Simplify the following using the values of the cubes 1 to 20 from the above table, (4)3 – (1)3 + (5)3
Solution:
= (4)3 – (1)3 + (5)3
= 64 – 1 + 125 {Using the value of cubes 1 to 20}
= 188
Problem 3: Simplify the following using the values of the cubes 1 to 20 from the above table, (14)3 – (9)3 + (15)3
Solution:
= (14)3 – (9)3 + (15)3
= 2744 – 729 + 3375 {Using the value of cubes 1 to 20}
= 2390
Problem 4: How much water does a fish tank hold that is in the shape of a cube with sides 10 cm?
Solution:
Given,
- Side of Cubical Fish Tank (a) = (a)3
(a)3 = (10)3 = 1000 cm3 = 1000 ml
We know that 1 ml = 1 cc
1000 cc = 1000 ml = 1 liter
Thus, the volume of the fish tank is 1 liter.
FAQs on Cubes 1 to 20
Q1: What are Cubes 1 to 20?
Answer:
The cube of 1 to 20 are the cubes of all natural number from 1 to 20, i.e. is contains the cube of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, and 20.
Q2: What are the Methods to Calculate Cubes?
Answer:
The cubes of the number are calculated using the methods that are,
- By Multiplying the Number Itself
- Using Algebric identites
Q3: What is the Cube of 9?
Answer:
The cube of 9 is,
93 = 9 × 9 × 9 = 729
Q4: What is the Cube of 15?
Answer:
The cube of 15 is,
153 = 15 × 15 × 15 = 25875
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