Cubes And Cube Roots Test

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Cubes And Cube Roots Test - 4

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Weekly Quiz Competition

Question 1
1 / -0

Three numbers are in the ratio 2 : 3 : 5. The sum of their cubes is 10240. The numbers are

A
2, 3 and 5

B
4, 6 and 10

C
6, 9 and 15

D
8, 12 and 20

Solution

Let the numbers be 2a, 3a and 5a.
According to the question:

8a³+ 27a³+ 125a³= 10240
160a³= 10240
a³= 64
a = 4

Therefore, the numbers are:
2a = 2 × 4 = 8
3a = 3 × 4 = 12
5a = 5 × 4 = 20
Question 2
1 / -0

The cube of a two-digit number contains

A
four digits in every case

B
three digits in every case

C
either three digits or four digits

D
anywhere from four digits to six digits

Solution

The cube of a two-digit number contains anywhere from four digits to six digits.

For example: Cube of the smallest two-digit number 10³= 1000 (four digits), and cube of the largest two-digit number 99³= 970299 (six digits)
Question 3
1 / -0

The cube of an even natural number is always ___________.

A
even

B
odd

C
either even or odd

D
prime

Solution

The cube of an even natural number is always even.

For example: 2³ = 8 (even), 4³ = 64(even), 6³ = 216 (even)
Question 4
1 / -0

If each side of a cubical gift box is 4.5 cm, then the volume of the box is ___________ m³.

A
9.1125 × 10^-6

B
91.125 × 10^-6

C
0.91125 × 10^-6

D
911.25 × 10^-6

Solution

Each side of the cubical gift box = 4.5 cm
Volume of the cubical gift box = 4.5 × 4.5 × 4.5 × 10^-6= 91.125 × 10^-6 m³.
Question 5
1 / -0

The units digit of the cube root of 21952 is

A
6

B
8

C
3

D
9

Solution

21952 = 4 x 4 x 4 x 7 x 7 x 7
So, cube root of 21952 = 4 x 7 = 28
Hence, units digit is 8.
Question 6
1 / -0

The volume of a cubical box of side d is twenty-five times d. Find the value of d, such that d ≠ 0 and d ≠ - 5.

A
5

B
4

C
6

D
7

Solution

According to the question:
d³= 25d
d³ - 25d = 0
d(d - 5²) = 0
d(d - 5)(d + 5) = 0
d = 0, d = 5, d = -5

Since d ≠ 0 and d ≠ -5, therefore the only possible value of d is 5.
Question 7
1 / -0

Two Rubik's cubes have their volumes in the ratio of 64 : 729. Find the ratio of the area of each face of the first cube to area of each face of the second cube.

A
12 : 27

B
16 : 49

C
14 : 27

D
16 : 81

Solution

Let the volume of the first Rubik's cube with side a₁ be 64 cu. units
Let the volume of the second Rubik's cube with side a₂ be 729 cu. units.
So, a₁³_: a₂³
= 64 : 729
So, a₁ : a₂ = 4 : 9

Area of each face of first cube = a₁²
Area of each face of second cube = a₂²
Required ratio = a₁² : a₂² = 16 : 81

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Re-Attempt Weekly Quiz Competition

Cubes And Cube Roots Test - 4

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Cubes And Cube Roots Test - 4

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SHARING IS CARING

Question 1

2, 3 and 5

4, 6 and 10

6, 9 and 15

8, 12 and 20

Solution

Question 2

four digits in every case

three digits in every case

either three digits or four digits

anywhere from four digits to six digits

Solution

Question 3

even

odd

either even or odd

prime

Solution

Question 4

9.1125 × 10-6

91.125 × 10-6

0.91125 × 10-6

911.25 × 10-6

Solution

Question 5

6

8

3

9

Solution

Question 6

5

4

6

7

Solution

Question 7

12 : 27

16 : 49

14 : 27

16 : 81

Solution

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9.1125 × 10^-6

91.125 × 10^-6

0.91125 × 10^-6

911.25 × 10^-6