This set of Mathematics Multiple Choice Questions & Answers (MCQs) focuses on “Cubes”.

1. What can be general formula to find cube of any number?

a) (a±b)^{2}

b) a^{2}

c) (a±b)^{3}

d) b

View Answer

Explanation: The general formula of finding square of any number is (a±b)

^{3}. We need to express the given number whose cube needs to be found in the form of (a±b). We can then use the formula:

(a±b)

^{3}= a

^{3}± 3a

^{2}b+3ab

^{2}± b

^{3}.

2. What form can be used to find cube of 13?

a) (10+3)^{3}

b) (10-3)^{3}

c) (10+3)

d) (10-3)

View Answer

Explanation: The number 13 can be represented in form 10 + 3, this will help us to calculate the cube of the number. This method would help us eliminate the traditional method of multiplying the number with itself.

3. 89^{3} = ____

a) (90-1)^{2}

b) (90-1)^{3}

c) 1^{2}

d) 9^{2}

View Answer

Explanation: If we must find the cube of the 89, we use the second variation i.e.(90-1)

^{3}. This would help us and make the calculations easier instead of multiplying the number with itself thrice.

Therefore (90-1)

^{3}= 90

^{3}– 3 × 90

^{2}× 1 + 3 × 90 × 1

^{2}– 1

^{3}

Therefore (90-1)

^{3}= 729000 – 24300 + 270 – 1

Therefore (90-1)

^{3}= 704969.

4. Find the cube of 32.

a) 32768

b) 37968

c) 32769

d) 35937

View Answer

Explanation: To find cube of 32, we would use the form

Therefore (30+2)

^{3}= 30

^{3}+ 3 × 30

^{2}× 2 + 3 × 30 × 2

^{2}+ 2

^{3}

Therefore (30+2)

^{3}= 27000 + 5400 + 360 + 8

Therefore (30+2)

^{3}= 32768

5. Calculate the cube of 201.

a) 8120604

b) 8120609

c) 8120600

d) 8120601

View Answer

Explanation: In the multiple-choice question, we can eliminate three options by mere observation. The unit place of cube of 201 should be 1. The only option which has 1 in unit place is 8120601. The other options are incorrect by mere observation.

6. 34^{3} = _____

a) 39504

b) 39304

c) 35304

d) 34304

View Answer

Explanation: In order to calculate the cube of 34 we use the formula,

(a+b)

^{3}, where we consider a=30 and b=4

Therefore (30+4)

^{3}= 30

^{3}+ 3×30

^{2}× 4 + 3 × 30 × 4

^{2}+ 4

^{3}

Therefore (30+4)

^{3}= 27000 + 10800 + 1440 + 64

Therefore (30+4)

^{3}= 39304.

7. Which of below is not a perfect cube?

a) 125

b) 728

c) 729

d) 64

View Answer

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. For example, 4 is a natural number which multiplied with itself thrice gives us 64. Hence, 64 is a perfect cube. But we do not have a natural number which multiplied with itself thrice gives us 728. Hence, 728 is not a perfect cube.

8. How many perfect cubes exist between 1 and 100?

a) 4

b) 20

c) 16

d) 8

View Answer

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. There are 4 perfect cubes between 1 and 100. They are 1, 8, 27, 64.

9. How many perfect cubes exist between 1 and 1000?

a) 5

b) 20

c) 10

d) 15

View Answer

Explanation: Perfect cube is formed when a natural number is multiplied to itself thrice. There are 10 perfect cubes between 1 and 1000. They are 1, 8, 27, 64, 125, 216, 343, 512, 729 and 1000.

10. 57^{3} = _____

a) 1125

b) 1961

c) 3249

d) 5764

View Answer

Explanation: In order to calculate the cube of 57 we use the formula,

(a-b)

^{3}, where we consider a=60 and b=3

Therefore (60-3)

^{3}= 60

^{3}– 3 × 60

^{2}× 3 + 3 × 60 × 3

^{2}– 3

^{3}

Therefore (60-3)

^{3}= 216000 – 32400 + 1620 – 27

Therefore (60-3)

^{3}= 185193.

**Sanfoundry Global Education & Learning Series – Mathematics – Class 8**.

To practice all areas of Mathematics, __ here is complete set of 1000+ Multiple Choice Questions and Answers__.

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