## 1. Which of the following numbers is a perfect cube?

a) 64

b) 45

c) 35

d) 50

### Answer:

a) 64

### Explanation:

64 is a perfect cube since 4 x 4 x 4 = 64.

## 2. What is the cube root of 27?

a) 2

b) 4

c) 3

d) 5

### Answer:

c) 3

### Explanation:

Since 3 x 3 x 3 = 27, the cube root of 27 is 3.

## 3. Which number when cubed gives 125?

a) 6

b) 4

c) 5

d) 3

### Answer:

c) 5

### Explanation:

5 x 5 x 5 = 125.

## 4. If the volume of a cube is 64 cm^3, what is the length of one side?

a) 8 cm

b) 4 cm

c) 6 cm

d) 3 cm

### Answer:

b) 4 cm

### Explanation:

The cube root of 64 is 4, which is the length of one side.

## 5. The smallest natural number by which 392 must be multiplied so that the product is a perfect cube is:

a) 7

b) 8

c) 9

d) 6

### Answer:

a) 7

### Explanation:

Prime factorization of 392 is 2 x 2 x 2 x 7 x 7. For a perfect cube, we need one more 7.

## 6. The cube root of 1 is:

a) 0

b) 1

c) 2

d) 3

### Answer:

b) 1

### Explanation:

1 x 1 x 1 = 1.

## 7. Which of the following is not a perfect cube?

a) 0

b) 1

c) 2

d) 8

### Answer:

c) 2

### Explanation:

2 cannot be expressed as a product of a number three times.

## 8. The volume of a cube with side 10 cm is:

a) 10 cm^3

b) 100 cm^3

c) 1000 cm^3

d) 10000 cm^3

### Answer:

c) 1000 cm^3

### Explanation:

Volume = side^3 = 10 x 10 x 10 = 1000 cm^3.

## 9. What is the smallest cube number greater than 0?

a) 1

b) 8

c) 9

d) 2

### Answer:

a) 1

### Explanation:

1^3 = 1.

## 10. Which of the following numbers is both a perfect square and a perfect cube?

a) 16

b) 81

c) 36

d) 64

### Answer:

d) 64

### Explanation:

64 = 8 x 8 (perfect square) and 64 = 4 x 4 x 4 (perfect cube).

## 11. If the side of a cube is tripled, its volume becomes:

a) 3 times

b) 9 times

c) 27 times

d) 81 times

### Answer:

c) 27 times

### Explanation:

New volume = (3s)^3 = 27s^3.

## 12. The cube of zero is:

a) 0

b) 1

c) Indeterminate

d) Not defined

### Answer:

a) 0

### Explanation:

0 x 0 x 0 = 0.

## 13. The cube root of a negative number:

a) Is negative

b) Is positive

c) Is zero

d) Does not exist

### Answer:

a) Is negative

### Explanation:

The cube root of a negative number is negative.

## 14. The cube root of 0.008 is:

a) 0.2

b) 0.02

c) 2

d) 20

### Answer:

b) 0.02

### Explanation:

(0.02 x 0.02 x 0.02) = 0.000008 or 0.008.

## 15. The number of 3-digit perfect cubes is:

a) 2

b) 3

c) 4

d) 5

### Answer:

a) 2

### Explanation:

They are 125 and 216.

## 16. Which of the following numbers will have the units digit the same as that in the cube of 3?

a) 6

b) 7

c) 9

d) 8

### Answer:

d) 8

### Explanation:

The cube of 3 is 27.

## 17. The cube of a negative integer is always:

a) Positive

b) Negative

c) Zero

d) None of the above

### Answer:

b) Negative

### Explanation:

Negative x Negative x Negative = Negative.

## 18. The cube root of 1/27 is:

a) 1/3

b) 1

c) 3

d) 1/9

### Answer:

a) 1/3

### Explanation:

(1/3 x 1/3 x 1/3) = 1/27.

## 19. If 2x^3 = 64, then x is:

a) 2

b) 3

c) 4

d) 8

### Answer:

c) 4

### Explanation:

2(4 x 4 x 4) = 2 x 64 = 128.

## 20. The total number of perfect cubes up to 1000 is:

a) 10

b) 12

c) 8

d) 14

### Answer:

b) 12

### Explanation:

From 1^3 to 12^3, there are 12 perfect cubes.