Cubes And Cube Roots Test

Result

Cubes And Cube Roots Test - 6

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Weekly Quiz Competition

Question 1
1 / -0

What is the unit digit of (23173)³ + (743129)³?

A
9

B
7

C
2

D
6

Solution

Unit digit of (23173)³ = Unit digit of 3³ = 7
Unit digit of (743129)³ = Unit digit of 9³ = 9
Adding unit digits,
7 + 9 = 16
The unit digit of (23173)³ + (743129)³= 6
Question 2
1 / -0

If ÷ = x, then the value of x is

A
42.4

B
53.3

C
63.3

D
65.1

Solution

÷ = x
= ÷
= 19 ÷ 0.3
= 19 × = 63.3
Question 3
1 / -0

If 343z⁴ = z⁷, the value of z is

A
1

B
5

C
7

D
9

Solution

343z⁴ = z⁷
343 = z⁷ ÷ z⁴
343 = z^(7-4)
343 = z³
z = 7
Question 4
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 5
1 / -0

A teacher wrote a perfect cube number on the board. A student copied it on his notebook and by mistake he forgot to copy 2 digits and wrote the number as 140AB8. The teacher asked to find the sum of digits of the cube root of the number. What was the sum?

A
5

B
7

C
2

D
9

Solution

140 AB8
Step 1: Take a group as AB8.
Last digit is 8 or
So, units digit of cube root of the number is 2.
Step 2: Take another group 140.
125 < 140 < 216
Step 3: Take the smallest cube-root which is 5 in this case.
So, tens place of the number is 5.
Cube root of number = 52
Sum of digits of the cube root of the number = 5 + 2 = 7.
Question 6
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 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

Three numbers are in the ratio 2 : 5 : 6. The sum of their cubes is 9423. The numbers are

A
16, 40, 48

B
8, 20, 24

C
6, 15, 18

D
12, 30, 36

Solution

Let the numbers be 2x, 5x and 6x.
(2x)³ + (5x)³ + (6x)³ = 8x³ + 125x³ + 216x³
349 x³= 9423
x³ = 27
x = 3
The numbers are:
2x = 2 × 3 = 6
5x = 5 × 3 = 15
6x = 6 × 3 = 18
Question 9
1 / -0

The cube of a three-digit number will contain

A
5 digits

B
6 digits

C
5 or 6 digits

D
7, 8 or 9 digits

Solution

Three-digit numbers range from 100 to 999.
Cube of 100 = 10,00,000
Cube of 999 = 99,70,02,999
Hence, number of digits will range from 7 to 9.
Question 10
1 / -0

The cube of an even natural number is always

A
even

B
odd

C
even or odd

D
can't say

Solution

The cube of an even natural number is always even.
For example:
Cube of 2 = 2 × 2 × 2 = 8
Cube of 4 = 4 × 4 × 4 = 64
Cube of 6 = 6 × 6 × 6 = 216 and so on.
Question 11
1 / -0

The length of each side of a cube is 4.6 cm. Its volume is

A
96.337 cm³

B
97.026 cm³

C
97.336 cm³

D
97.733 cm³

Solution

Side of the cube = 4.6 cm
Volume = (side)³
4.6 × 4.6 × 4.6 = 97.336 cm³
Question 12
1 / -0

What is the smallest number by which 3087 must be divided so that the quotient obtained is a perfect cube?

A
6

B
9

C
11

D
12

Solution

3087 = 7 × 7 × 7 × 9
To obtain a perfect cube, we need to divide 3087 by 9.
So, the correct answer is 9.
Question 13
1 / -0

The cube root of a number 'x' is 5 more than the 4^th multiple of 5. What is the cube root of a number 'y' such that 'y' is 8764 more than 'x'?

A
33

B
31

C
29

D
27

Solution

= 5 + (4 x 5)
= 5 + 20 = 25
x = (25)³ = 15625
y = 8764 + 15625 = 24389
(y)^1/3 = (24389)^1/3 = (29 x 29 x 29)^1/3 = 29
Question 14
1 / -0

Two cubes have volume in the ratio 8 : 64. The ratio of their surface areas is

A
2 : 5

B
2 : 3

C
1 : 4

D
3 : 7

Solution

Ratio of volumes = 8 : 64

Ratio of sides =
=

Surface area of a cube = 6a²(where a = side of the cube)

Ratio of surface areas =
=

= = 1 : 4
Question 15
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 16
1 / -0

Akul gave a Mathematical problem to Yamini;
The difference of two perfect cubes is 387. If the cube root of the greater of the two numbers is 8, find the cube root of the smallernumber.

Help Yamini to find the answer.

A
4

B
5

C
6

D
7

Solution

The cube root greater number is 8. So, the greater number will be 512.
Now, the difference is 387. Therefore, the second perfect cube is 512 - 387 = 125.
Thus, cube root of smaller number is 5.
Question 17
1 / -0

A blacksmith has to make 13 smaller cubes each of side 6 cm after melting the larger cuboidal box of dimensions 12 cm × 13 cm × 21 cm. What will be the volume of the left over material after making new cubes?

A
720 cm³

B
468 cm³

C
331 cm³

D
321 cm³

Solution

Volume of the cuboid = 12 × 13 × 21 = 3276 cm³
Volume of 1 smaller cube = 6 × 6 × 6 = 216 cm³
Volume required for 13 smaller cubes = 13 × 216 = 2808 cm³
Volume of the left over material = 3276 - 2808 = 468 cm³
Question 18
1 / -0

A cubical box of volume 135 cm³ is cut into 5 smaller cubical boxes. What is the length of the side of each smaller cubical box formed?

A
3 cm

B
8 cm

C
11 cm

D
16 cm

Solution

Volume of large cubical box = 135 cm³
Now,
Volume of large cubical box = number of smaller cubical boxes formed x volume of one such small box
135 cm³= 5 × volume of one such small box
27 cm³= volume of one such small box
Therefore, side of each small cubical box = = 3 cm
Therefore, 3 cm is the correct answer.
Question 19
1 / -0

A cubical fish tank is used to keep fishes at an aquarium. The capacity of the fish tank is 46,656 m³. Find the depth of fish tank.

A
36 m

B
45 m

C
58 m

D
63 m

Solution

Volume of cubical fish tank = (Side)³
46,656 m³= (Side)³

Side = = 36 m

Therefore, the fish tank is 36 m deep.
Question 20
1 / -0

If the side of a cube is 7 cm, what is its volume in mm³?

A
3,73,000 mm³

B
2,89,800 mm³

C
3,43,000 mm³

D
3,82,500 mm³

Solution

Volume of the cube = (side)³= (7 cm)³ = 343 cm³Now, as 1 cm = 10 mm
343 cm³ = 3,43,000 mm³So, the volume of cube is 3,43,000 mm³.
Question 21
1 / -0

Which of the following statements is INCORRECT?

(a) A cube shaped container whose volume is 1,32,651 m³has a side of 51 m.(b) The smallest number by which 392 must be multiplied to make it a perfect cube is 7.
(c) The difference between the sum of cubes of two consecutive numbers and cube of 5 is 37. The numbers are 3 and 4.

A
a

B
b

C
c

D
Both a and b

Solution

(a) Volume of cube = 1,32,651 m³
Let the side of cube = x m
Volume of cube = (side)³=(x)³1,32,651 = x³
= 51 m
So, this statement is correct.

(b) Number = 392

The factors of 392 =
So, to make it a perfect cube, we need to multiply 392 with 7.

(c) Given numbers = 3 and 4
Cube of 3 = 3³ = 27
Cube of 4 = 4³ = 64
Sum = 64 + 27 = 91
Cube of 5 = 5³ = 125
Difference = 125 - 91 = 34
However, the given difference is 37.

So, statement (c) is incorrect.
Question 22
1 / -0

Find the cube roots of:

(i) A = 0.004096
(ii) B = 12.167
(iii) C = 19.683
(iv) D = 29.791

A

A 0.16

B 2.3

C 2.7

D 3.1

B

A 1.6

B 2.7

C 3.1

D 2.3

C

A 1.6

B 2.7

C 2.3

D 3.1

D

A 2.7

B 1.6

C 3.1

D 2.3

Solution

Cube root of 0.004096 =

Cube root of 12.167 =

Cube root of 19.683 =

Cube root of 29.791 =

Question 23

1 / -0

Match the following:

Column-I	Column-II
A. The smallest number that should be added to 123 to make it a perfect cube is	(i) 6
B. The smallest number that should be subtracted from 21,957 to make it a perfect cube is	(ii) 3
C. The smallest number that should be added to 2,191 to make it a perfect cube is	(iii) 2
D. The smallest number that should be subtracted from 10,651 to make it a perfect cube is	(iv) 5

A (iii)

B (iv)

C (i)

D (ii)

A (i)

B (ii)

C (iii)

D (iv)

A (ii)

B (iv)

C (i)

D (iii)

A (iv)

B (ii)

C (iii)

D (i)

Solution

(A) 4³ < 123 < 5³
Perfect cube just greater than 123 is 125. So, the smallest number that should be added to 123 to make it a perfect cube is 2.

(B) 28³ < 21,957 < 29³
Perfect cube less than 21,957 is 21,952. So, the smallest number that should be subtracted from 21,957 to make it a perfect cube is 5.

(C) 12³ < 21,191 < 13³
Perfect cube just greater than 2,191 is 2,197. So, the smallest number that should be added to 2,191 to make it a perfect cube is 6.

(D) 22³ < 10,651 < 23³
Perfect cube less than 10,651 is 10,648. So, the smallest number that should be subtracted from 10,651 to make it a perfect cube is 3.

Question 24
1 / -0

Evaluate the following :

(i)

(ii)

(iii)

A

(i) (ii) (iii)

2.9 -0.28 2.24

B

(i) (ii) (iii)

0.29 0.28 -2.98

C

(i) (ii) (iii)

0.29 2.9 -2.89

D

(i) (ii) (iii)

29 0.30 2.24

Solution

(i)

=

= = 0.29

(ii) Cube root of 4,913 = 17
Cube root of 6.859 = 1.9
Cube root of 4,096 = 16
= 17 + 1.9 - 16
= 2.9

(iii)
=

=

=

=

=

= -2.89
Question 25
1 / -0

Which of the following statement(s) is/are CORRECT?

Statement - 1: Cube root of 6,81,472 is an irrational number.
Statement - 2: Cube of an odd number may or may not be an odd number.

A
Only statement 2.

B
Only statement 1.

C
Both statements 1 and 2.

D
Neither statement 1 nor 2.

Solution

1. Cube root of 6,81,472 is 88 which is a rational number. Any real number that cannot be written in a fraction form is an irrational number. These numbers include the non-terminating, non-repeating decimals, such as pi (3.1515926).
2. Cube of an odd number is always an odd number.
E.g : 3³ = 27
5³ = 125
7³ = 343
So, both the statements are incorrect.