Cubes And Cube Roots(8th Grade > Mathematics ) Questions and answers for exam Preparation

8th Grade > Mathematics

CUBES AND CUBE ROOTS MCQs

Total Questions : 57 | Page 2 of 6 pages

Question 11. The volume of a closed cubical tank is 1331 cubic metres. Find the cost of painting its complete surface area from outside at the rate of ₹ 10 per square meter.

7260
7240
7000
7280

Discuss Question

Answer: Option A. -> 7260
:
A
Let the side of the given cubical tank be 'a' metres .
Volume of the given cube is

a \times a \times a

By prime factorization, we get cube root of 1331 as 11
Surface area of each side of a cube is

a \times a

Total surface area of the cube is

6 \times a \times a

Cost incurred is then

10 \times 6 \times 11 \times 11

=₹7260

Question 12. The difference of cubes of two consecutive numbers is always divisible by 3.

True
False
441
788

Discuss Question

Answer: Option B. -> False
:
B
Take two numbers, for example, 2 and 1 and check.
The difference of cubes of 2 and 1 is 7, which is not divisible by 3.

Question 13. If the value of

(\frac{a^{3} - b^{3}}{a^{3} + b^{3}})

when a = 7 and b = 2 is

\frac{335}{p}

, then p is 321.

True
False
441
788

Discuss Question

Answer: Option B. -> False
:
B

a^{3}

b^{3}

(a - b)

(

a^{2}

a b

b^{2}

)

a^{3}

b^{3}

(a + b)

(

a^{2}

a b

b^{2}

)
Puting the values of a and b,weget the value of p as 351.
Alternatively, we can observe that since a and b are positive, so denominator has to be greater than numerator. Thus,

a^{3}

b^{3}

will be greater than

a^{3}

b^{3}

Question 14. The units digit in the expansion of

16^{3}

is
___

Discuss Question

:
The units digit of the cube of any number with 6 in its unit's place is always 6. Alternatively, we can see that 6 when multiplied with itself three times yields 216, whose last digit is 6.

Question 15. What is the units digit of the cube of the number whose unit digit is 7?

Discuss Question

Answer: Option A. -> 3
:
A
The units digit of the cube of 7 i.e.343 is 3.
Thus, the units digit of the cube of the number whose unit digit is 7 will be 3.

Question 16. With what number should 1715 be divided to get a perfect cube?

1
7
5
Already a perfect cube

Discuss Question

Answer: Option C. -> 5
:
C
For a numberto be a perfect cube, its prime factors should be expressed as triplets
By prime factorization,we get 1715 = 7×7×7×5
We have three 7’s but only one 5 so we need to divide the number by 5.

Question 17. 100 is the smallest square number that is the sum of cubes of 4 consecutive natural numbers.

True
False
5
Already a perfect cube

Discuss Question

Answer: Option A. -> True
:
A
100 =

10^{2}

1^{3}

2^{3}

3^{3}

4^{3}

= 1+8+27+64

Question 18. Anshul and Balendu have 50 cubes of side 1 cm. They decided to make a larger cube by joining these smaller cubes. The number of larger cubes (all of different sizes) they can make is
___

Discuss Question

:
Since the side of the smaller cube is 1 cm, its volume will be 1 cubic cm.
We know that the volume of cubes of sides 1,2,3,4,... are 1,8,27,64...cubic cm.
But Anshul and Balendu have only 50 small cubes, so they can make cubes of 3 sizes with the help of 1,8 and 27 smaller cubes.
It should be noted that (50-1-8-27) = 14 smaller cubes will be left unused.

Question 19. What should be multiplied to 43200 to make it a perfect cube?

2
3
5
Already a perfect cube

Discuss Question

Answer: Option C. -> 5
:
C
For a number to be a perfect cube, its prime factors should be in the form of triplets
By prime factorization, 43200 =

2^{6}

3^{3}

5^{2}

Only two 5’s are there so we need one more 5 to make a triplet.
So if 43200 is multiplied by 5, we get a perfect cube.

Question 20. Which of these is not a perfect cube?

343
1331
512
81

Discuss Question

Answer: Option D. -> 81
:
D
By prime factorization, we have

343 = 7 \times 7 \times 7 1331 = 11 \times 11 \times 11 512 = 8 \times 8 \times 8 81 = 3 \times 3 \times 3 \times 3

For a number to be a perfect cube ,each of its factors must be repeated thrice.
343, 1331 and 512 are the perfect cubes of 7, 11 and 8 respectively, whereas 81 is not, as 3 is repeating 4 times which is not a triplet.
81 is not a perfect cube.