# Mathematics Questions and Answers – Cubes

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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) a2
c) (a±b)3
d) b

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= a3 ± 3a2 b+3ab2 ± b3.

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)

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. 893 = ____
a) (90-1)2
b) (90-1)3
c) 12
d) 92

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 = 903 – 3 × 902 × 1 + 3 × 90 × 12 – 13
Therefore (90-1)3 = 729000 – 24300 + 270 – 1
Therefore (90-1)3 = 704969.
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4. Find the cube of 32.
a) 32768
b) 37968
c) 32769
d) 35937

Explanation: To find cube of 32, we would use the form
Therefore (30+2)3 = 303 + 3 × 302 × 2 + 3 × 30 × 22 + 23
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

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. 343 = _____
a) 39504
b) 39304
c) 35304
d) 34304

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 = 303 + 3×302 × 4 + 3 × 30 × 42 + 43
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

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

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

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. 573 = _____
a) 1125
b) 1961
c) 3249
d) 5764

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 = 603 – 3 × 602 × 3 + 3 × 60 × 32 – 33
Therefore (60-3)3 = 216000 – 32400 + 1620 – 27
Therefore (60-3)3 = 185193.

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