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
View Answer

Answer: a
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.
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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

Answer: a
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
View Answer

Answer: b
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
View Answer

Answer: a
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
View Answer

Answer: d
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.
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6. 343 = _____
a) 39504
b) 39304
c) 35304
d) 34304
View Answer

Answer: b
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
View Answer

Answer: b
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.
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8. How many perfect cubes exist between 1 and 100?
a) 4
b) 20
c) 16
d) 8
View Answer

Answer: a
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

Answer: a
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.
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10. 573 = _____
a) 1125
b) 1961
c) 3249
d) 5764
View Answer

Answer: c
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.

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

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter