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.