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MCQ (with Solutions): Cubes & Cubes Roots | Mathematics (Maths) Class 8 PDF Download

Q1: What can be general formula to find cube of any number?
(a) (a±b)³
(b) a²
(c) (a±b)²
(d) b

Ans: (a)
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.

Q2: 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

Ans: (a)
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.

Q3: 89³ = ____
(a) (90-1)²
(b) (90-1)³
(c) 1²
(d) 9²

View Answer

Ans: (b)
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.

Q4: Find the cube of 32.
(a) 32768
(b) 37968
(c) 32769
(d) 35937

View Answer

Ans: (a)
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

Q5: Calculate the cube of 201.
(a) 8120604
(b) 8120609
(c) 8120600
(d) 8120601

View Answer

Ans: (d)
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.

Q6: 34³ = _____
(a) 39504
(b) 39304
(c) 35304
(d) 34304

View Answer

Ans: (b)
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.

Q7: Which of below is not a perfect cube?
(a) 125
(b) 728
(c) 729
(d) 64

View Answer

Ans: (b)
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.

Q8: How many perfect cubes exist between 1 and 100?
(a) 4
(b) 20
(c) 16
(d) 8

View Answer

Ans: (a)
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.

Q9: How many perfect cubes exist between 1 and 1000?
(a) 5
(b) 20
(c) 10
(d) 15

View Answer

Ans: (a)
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.

Q10: 57³ = _____
(a) 193753
(b) 176452
(c) 185193
(d) 186743

View Answer

Ans: (c)
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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FAQs on MCQ (with Solutions): Cubes & Cubes Roots - Mathematics (Maths) Class 8

1. What is a cube root?

Ans. A cube root is a number that when multiplied by itself three times, gives the original number. For example, the cube root of 27 is 3 because 3 x 3 x 3 = 27.

2. How do you find the cube of a number?

Ans. To find the cube of a number, you simply multiply the number by itself twice. For example, the cube of 5 is 5 x 5 x 5 = 125.

3. What is the difference between a cube and a cube root?

Ans. A cube is the result of multiplying a number by itself three times, while a cube root is the inverse operation, finding the number that when multiplied by itself three times gives the original number.

4. How can cubes be used in real life?

Ans. Cubes are commonly used in building construction to create shapes like bricks, blocks, and pillars. They are also used in mathematics to calculate volumes of 3D shapes.

5. Is it possible to find the cube root of negative numbers?

Ans. Yes, it is possible to find the cube root of negative numbers. The cube root of a negative number is a negative number itself.

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