Cubes and Cube Roots Test

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Cubes and Cube Roots Test - 5

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Weekly Quiz Competition

Question 1
1 / -0

How many cubes of side 3 cm each can be packed in a cubical box with inner side of 6 cm?

A
10

B
6

C
8

D
12

Solution

Side of the smaller cube = 3 cm
Volume of the smaller cube = 3 × 3 × 3 = 27 cm³
Side of the bigger cube (box) = 6 cm
Volume of the bigger cube (box) = 6 × 6 × 6 = 216 cm³
Number of smaller cubes which can be packed in the bigger cubical box = = 8
Hence, option 3 is correct.
Question 2
1 / -0

The prime factorisation of a number is of the form A B C D. If A = 2 3 3, B = 3 2 7 and C = 5 5 7 2, then what will be the smallest value of D such that the product is a perfect cube?

A
2 2 3

B
5 7

C
2 5 7

D
5 5

Solution

A B C =
5 and 7 are not grouped as triplets.
So, to make them triplets, we need one 5 and one 7.
D = 5 7
Question 3
1 / -0

What is the smallest number by which 8712 must be divided, so that the quotient obtained is a perfect cube?

A
33

B
11

C
1089

D
2424

Solution

8712 = 2 × 2 × 2 × 3 × 3 × 11 × 11
3 and 11 are not grouped as triplets.
So, the smallest number is 3 × 3 × 11 × 11 = 1089.
Question 4
1 / -0

What is the smallest number by which (2 3 6)³ (2 3)² must be divided, so that the quotient is a perfect cube?

A
2 3

B
(2 3)²

C
(3 3)²

D
(2 2)

Solution

In (2 3 6)³ (2 3)², (2 3)²is not grouped as triplets. So, we divide the number by (2 3)².
Question 5
1 / -0

The cube root of 753571 is of the form A B, where A and B are prime numbers. What are the values of A and B?

A
7, 13

B
5, 13

C
5, 7

D
5, 11

Solution

753571 = 7 7 7 13 13 13
= 7³13³
= (7 13)³
Or
A = 7
B = 13
Question 6
1 / -0

Amrita has a 6-digit number with her. By mistake, she erased one digit out of that number. The number remained as 571A87. What is the ten's place of the cube root of the number?

A
6

B
9

C
8

D
7

Solution

Take 571 as a group for ten's place of cube root of the number.
Now, cube of 8 is 512 and cube of 9 is 729.
571 lies between 512 and 729.
Also, 8 is smaller than 9.
So, ten's place of the cube root of the number is 8.
Question 7
1 / -0

A perfect cube number is given as 10AB8. What are the respective values of A and B?

A
6 and 4

B
4 and 6

C
3 and 2

D
2 and 3

Solution

Step 1: In AB8, the units digit is 8.
Or, = 2
So, the units place of cube root of the number is 2.
Step 2: 8 < 10 < 27
2³ < 10 < 3³
2 is smaller than 3.
So, tens place of cube root of the number is 2.
The cube root of the number 10AB8 is 22.
Or, (22)³ = 10AB8
Or, 10648 = 10AB8
A = 6 and B = 4
Question 8
1 / -0

What is the value of ?

A
66

B

C
33

D

Solution

= 2 3 11 = 66
Question 9
1 / -0

The prime factorisation of a number is 2 5 3 2 7 7 3 2 7 5 5. Which of the following is true regarding the number?

A
It is a perfect cube of 210.

B
It can be made a perfect cube by multiplying it by 3.

C
It is a perfect cube of 212.

D
It can be made a perfect cube by dividing it by 3.

Solution

Since 3 cannot be grouped as a triplet, it is not a perfect cube; but it can be made a perfect cube by multiplying it by 3.
Question 10
1 / -0

What is the smallest number which when multiplied by 3600 will give a perfect cube as the product?

A
100

B
60

C
50

D
40

Solution

3600 = 2 × 3 × 2 × 5 × 2 × 3 × 2 × 5
Pairing up, we get
3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5
So, to obtain a perfect cube, we need to multiply 3600 by 2 × 2 × 3 × 5 = 60.
So, the correct answer is 60.
Question 11
1 / -0

Which of the following statements is/are true?
(I) Cube of any odd number is even.
(II) A perfect cube does not end with two zeroes.

A
Both (I) and (II) are true

B
Both (I) and (II) are false

C
Only (I) is true

D
Only (II) is true

Solution

(i) Cube of an odd number is even. (False)

Cube of an odd number is always odd.

e.g. (11)³ = 11 × 11 × 11 = 121 × 11

= 1331

(ii) A perfect cube does not end with two zeroes. (True)

A perfect cube will end with 3, 6, 9 .......... zeroes.

e.g. 30³ = 27000 50³ = 125000

So, only (II) is correct.
Question 12
1 / -0

Which of the following options is the same as ?

A
x²

B
x

C
1

D
1/x

Solution
Question 13
1 / -0

If is subtracted from the sum of , then what will be the result?

A
26

B
21

C
20

D
19

Solution

12 + 14 - 6 = 20
Question 14
1 / -0

What will you get when the cube root of 19,683 is added to the square root of 324 and the resultant is divided by the cube root of 729?

A
5

B
6

C
7

D
8

Solution

= 27
= 18

= 9
So,
Question 15
1 / -0

If the cube root of 512 is subtracted from the square root of 961, then what will be the result?

A
22

B
23

C
24

D
25

Solution

= 31
= 8
31 - 8 = 23