Boost Math knowledge and enhance the creativity of math problem solving with this fun Worksheet on Cube. All the Questions, Answers are provided here along with clear explanations. Follow the steps to solve math problems and learn the tricks to solve the cube of a number. Students can easily understand How to Find a Cube of the Number with the detailed explanation. We included all the concepts of a cube of a decimal number, the cube of finding perfect cubes, and also the process of finding the cubes of odd and even numbers.

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1. Evaluate the cube of a number

(i) (9)³ (ii) (14)³ (iii) (26)³ (iv) (50)³

## Solution:

(i) (9)³

The given number is 9.

Multiply 9 three times to get a Cube of 9.

Cube of 9 = (9)³ = 9 × 9 × 9

Cube of 9 = 729

(ii) (14)³

The given number is 14.

Multiply 14 three times to get a Cube of 14.

Cube of 14 = (14)³ = 14 × 14 × 14

Cube of 14 = 2744

(iii) (26)³

The given number is 26.

Multiply 26 three times to get a Cube of 26.

Cube of 26 = (26)³ = 26 × 26 × 26

Cube of 26 = 17576

(iv) (50)³

The given number is 50.

Multiply 50 three times to get a Cube of 50.

Cube of 50 = (50)³ = 50 × 50 × 50

Cube of 50 = 125000

2. Find the cube of a decimal number

(i) (1.3)³ (ii) (3.6)³ (iii) (0.7)³ (iv) (0.03)³

## Solution:

(i) (1.3)³

The given decimal number is 1.3.

Multiply 1.3 three times to get a Cube of 1.3.

Cube of 1.3 = (1.3)³ = (1.3) × (1.3) × (1.3)

Cube of 1.3 = 2.197

(ii) (3.6)³

The given decimal number is 3.6.

Multiply 3.6 three times to get a Cube of 3.6.

Cube of 3.6 = (3.6)³ = (3.6) × (3.6) × (3.6)

Cube of 3.6 = 46.656

(iii) (0.7)³

The given decimal number is 0.7.

Multiply 0.7 three times to get a Cube of 0.7.

Cube of 0.7 = (0.7)³ = (0.7) × (0.7) × (0.7)

Cube of 0.7 = 0.343

(iv) (0.03)³

The given decimal number is 0.03.

Multiply 0.03 three times to get a Cube of 0.03.

Cube of 0.03 = (0.03)³ = (0.03) × (0.03) × (0.03)

Cube of 0.03 = 0.000027

3. Evaluate the cube of a fraction number

(i) (3/7)³ (ii) (11/10)³ (iii) (1/12)³ (iv) (1(4/10))³

## Solution:

(i) (3/7)³

The given fraction number is 3/7.

Multiply 3/7 three times to get a Cube of 3/7

Cube of 3/7 = (3/7)³ = (3/7) × (3/7) × (3/7)

Cube of 3/7 = (3 × 3 × 3)/(7 × 7 × 7)

Cube of 3/7 = 27/343

(ii) (11/10)³

The given fraction number is 11/10.

Multiply 11/10 three times to get a Cube of 11/10

Cube of 11/10 = (11/10)³ = (11/10) × (11/10) × (11/10)

Cube of 11/10 = (11 × 11 × 11)/(10 × 10 × 10)

Cube of 11/10 = 1331/1000

(iii) (1/12)³

The given fraction number is 1/12.

Multiply 1/12 three times to get a Cube of 1/12

Cube of 1/12 = (1/12)³ = (1/12) × (1/12) × (1/12)

Cube of 1/12 = (1 × 1 × 1)/(12 × 12 × 12)

Cube of 1/12 = 1/1728

(iv) (1(4/10))³

The given fraction number is 1(4/10).

1(4/10) = 14/10

Multiply 1(4/10) three times to get a Cube of 1(4/10)

Cube of 1(4/10) = (14/10)³ = (14/10) × (14/10) × (14/10)

Cube of 1(4/10) = (14 × 14 × 14)/(10 × 10 × 10)

Cube of 1(4/10) = 2744/1000

4. Find whether the given numbers are perfect cubes or not?

(i) 512 (ii) 5488 (iii) 686 (iv) 216

## Solution:

(i) 512

The given number is 512.

Separate 512 into different prime factors

The prime factors for 512 are 8, 8, 8.

512 = 8 × 8 × 8

Group prime factors of a 512 in triples of equal factors.

512 = (8 × 8 × 8)

There is one triple factor available in the prime factors of the given number.

Therefore, the given number is a perfect cube.

ii) 5488

The given number is 5488.

Separate 5488 into different prime factors

The prime factors for 5488 are 7, 7, 7, 4, 4.

5488 = 7 × 7 × 7 × 4 × 4

Group prime factors of a 5488 in triples of equal factors.

5488 = (7 × 7 × 7) × (4 × 4)

There are one triple factor and double factors available in the prime factors of the given number.

Therefore, the given number is not a perfect cube.

(iii) 686

The given number is 686.

Separate 686 into different prime factors

The prime factors for 686 are 7, 7, 7, 2.

686 = 7 × 7 × 7 × 2

Group prime factors of a 686 in triples of equal factors.

686 = (7 × 7 × 7) × (2)

There are one triple factor and single factor available in the prime factors of the given number.

Therefore, the given number is not a perfect cube.

(iv) 216

The given number is 216.

Separate 216 into different prime factors

The prime factors for 216 are 6, 6, 6.

216 = 6 × 6 × 6

Group prime factors of a 216 in triples of equal factors.

216 = (6 × 6 × 6)

There is one triple available in the prime factors of the given number.

Therefore, the given number is a perfect cube.

5. Which of the following are Cubes of Even Numbers and Odd Numbers?

(i) 64 (ii) 125 (iii) 1728 (iv) 1331

## Solution:

(i) 64

The given number is 64.

Find the prime factors of the given number 64.

The prime factors of 64 are 4, 4, 4

64 = 4 × 4 × 4

64 = 4³

4 is an even number

64 is a cube of an even number.

(ii) 125

The given number is 125.

Find the prime factors of the given number 125.

The prime factors of 125 are 4, 4, 4

125 = 5 × 5 × 5

125 = 5³

5 is an odd number

125 is a cube of an odd number.

(iii) 1728

The given number is 1728.

Find the prime factors of the given number 1728.

The prime factors of 1728 are 12, 12, 12

64 = 12 × 12 × 12

64 = (12)³

12 is an even number

1728 is a cube of an even number.

(iv) 1331

The given number is 1331.

Find the prime factors of the given number 1331.

The prime factors of 125 are 4, 4, 4

1331 = 5 × 5 × 5

1331 = 5³

5 is an odd number

1331 is a cube of an odd number.

6. What is the smallest number by which 84672 must be multiplied so that the product is a perfect cube?

## Solution:

To find the smallest number by which 84672 must be multiplied so that the product is a perfect cube, you need to find the prime factors of the given number.

The prime factors of the given number 84672 are 12, 12, 12, 7, 7

84672 = 12 × 12 × 12 × 7 × 7

84672 = (12)³ × 7 × 7

From above, by multiplying 7 the number 84672 becomes the perfect cube.

Therefore, the smallest number is 7.

7. What is the smallest number by which 36000 must be multiplied so that the product is a perfect cube?

## Solution:

To find the smallest number by which 36000 must be multiplied so that the product is a perfect cube, you need to find the prime factors of the given number.

The prime factors of the given number 36000 are 10, 10, 10, 6, 6

36000 = 10 × 10 × 10 × 6 × 6

36000 = (10)³ × 6 × 6

From above, by multiplying 6 the number 36000 becomes the perfect cube.

Therefore, the smallest number is 6.

8. Find the smallest number by which 2916 must be divided so that the quotient is a perfect cube?

## Solution:

To find the smallest number by which 2916 must be divided so that the product is a perfect cube, you need to find the prime factors of the given number.

The prime factors of the given number 2916 are 9, 9, 9, 2, 2

2916 = 9 × 9 × 9 × 2 × 2

2916 = (9)³ × 2 × 2

From above, by dividing 4 the number 2916 becomes the perfect cube.

Therefore, the smallest number is 4.

9. Find the smallest number by which 3456 must be divided so that the quotient is a perfect cube?

## Solution:

To find the smallest number by which 3456 must be divided so that the product is a perfect cube, you need to find the prime factors of the given number.

The prime factors of the given number 3456 are 6, 6, 6, 4, 4

3456 = 6 × 6 × 6 × 4 × 4

3456 = (6)³ × 4 × 4

From above, by dividing 16 the number 3456 becomes the perfect cube.

Therefore, the smallest number is 16.