CBSE Class 8 Mathematics Cubes and Cube Roots Assignment Set F

1. The value of 45³ – 65³ – 20³ is ____.
(A) 175500
(B) – 191500
(C) 170000
(D) – 170000
Answer : B

2. If ³√−2744 ÷ ³√0.008 = x, then the value of x is ____.
(A) 70
(B) – 70
(C) 14
(D) – 14
Answer : B

3. If

(A) 10/3
(B) −10/3
(C) 3/15
(D) Both (A) and (B)
Answer : D

4. How many cubes of side 2 cm can be packed in a cubical box with inner side equal to 4 cm?
(A) 6
(B) 4
(C) 8
(D) 2
Answer : C

5. Find the smallest natural number by which 1458 must be divided so that the quotient is a perfect cube.
(A) 4
(B) 2
(C) 6
(D) 8
Answer : B

6. In the five digit number 1b6a3, a is the greatest single digit perfect cube and twice of it exceeds b by 7. Then the sum of the number and its cube root is ____.
(A) 18700
(B) 11862
(C) 19710
(D) 25320
Answer : C

7. The value of

(A) −bc³/a²
(B) bc⁴/a²
(C) −ab⁴/c²
(D) −bc⁴/a²
Answer : D

8. Three numbers are in the ratio 2 : 3 : 5 to one another. The sum of their cubes is 54880. The numbers are______.
(A) 14, 21, 35
(B) 12, 15, 17
(C) 14, 18, 21
(D) 21, 28, 32
Answer : A

9. The cube of a 2-digit number will contain ________.
(A) 4 digits
(B) 5 digits
(C) 6 digits
(D) 4, 5 or 6 digits
Answer : C

10. The cube of an odd natural number is always _____.
(A) Even
(B) Odd
(C) Even or odd
(D) Can’t say
Answer : B

11. The length of each side of a cubical box is 2.4 m. Its volume is _____.
(A) 1.3824 × 10⁷ cu. cm
(B) 13.824 cu. cm
(C) 1.3824 × 10⁶ cu. cm
(D) 13.824 × 10⁴ cu. cm
Answer : A

12. The unit’s digit of the cube of a number is 9. The unit’s digit of its cube root is _____.
(A) 9
(B) 7
(C) 3
(D) 1
Answer : A

13. The cube of a number x is nine times of x, then find x, where x ≠ 0 and x ≠ –3.
(A) 8
(B) 2
(C) 4
(D) 3
Answer : D

14. Two cubes have volumes in the ratio 1 : 27. The ratio of the area of the face of one to that of the other is ____.
(A) 1 : 3
(B) 1 : 6
(C) 1 : 9
(D) 1 : 18
Answer : C

15. The smallest number by which 392 must be amultiplied so that the product is a perfect cube, is ____.
(A) 3
(B) 5
(C) 7
(D) 9
Answer : C

16. Mohit gave a problem to Samrath. Difference of two perfect cubes is 189. If the cube root of the smaller of the two numbers is 3, find the cube root of the larger number.
Help Samrath to answer the question.
(A) 4
(B) 6
(C) 8
(D) 10
Answer : B

17. A tank is in the form of a cube whose volume is 9261000 m3. Find the length of side of the tank.
(A) 230 m
(B) 250 m
(C) 210 m
(D) 180 m
Answer : C

18. Atul made a cuboid of plasticine. Length, breadth and height of the cuboid are
25 cm, 25 cm and 50 cm. How many minimum such cuboids he needs to make a perfect cube?
(A) 4
(B) 20
(C) 12
(D) 25
Answer : A

19. A rectangular cubical piece of metal of dimensions 2 cm × 3 cm × 4 cm is melted. Some more of the metal is added and it is made into a cube. The cube has integral measures for its sides. What is the minimum amount of metal that is added and what is the side of this cube?
(A) 10 cm³, 4 cm
(B) 3 cm³, 3 cm
(C) 11 cm³ 3 cm
(D) 4 cm³, 3 cm
Answer : B

20. To collect rain water, Mini made a cubical tank which can hold 91125 m3 water. She uses this water for watering the plants of her garden. What is the height of the tank?
(A) 50 m
(B) 25 m
(C) 45 m
(D) 40 m
Answer : C

21. Which of the following options is INCORRECT?
(A) Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500.
The numbers will be 5, 10, 15.
(B) The digit in the units place for the cube of a four digit number of the form xyz8 is 2.
(C) The smallest number by which 3600 be divided to make it a perfect cube is 450.
(D) None of these
Answer : D

22. Find the cube root of:
(i) 0.003375 = P .
(ii) 1.331 = Q .
(iii) 4.913 = R .
(iv) 15.625 = S .
         P            Q           R           S
(A) 0.215       1.31       2.7        2.55
(B) 0.115       1.11       1.17      3.25
(C) 0.15         1.1        1.7         2.5
(D) 0.25         1.21       2.17      4.15
Answer : C

23. Match the following

(A) P → (iii); Q → (i); R → (iv); S → (ii)
(B) P → (ii); Q → (iv); R → (i); S → (iii)
(C) P → (iii); Q → (i); R → (ii); S → (iv)
(D) P → (iii); Q → (iv); R → (ii); S → (i)
Answer : D

24. Evaluate the following.

     (i)              (ii)             (iii)
(A) 1              6.9             2/5
(B) 3              7.1             1/5
(C) 4              7.9             2/5
(D) 1              6.5             1/5
Answer : A

25. Which of the following statements is CORRECT ?
Statement - 1 : Cube root of 117.649 is a rational number.
Statement - 2 : Cube of an odd number may or may not be odd.
(A) Only Statement - 1
(B) Only Statement - 2
(C) Both Statement - 1 and Statement - 2
(D) Neither Statement - 1 nor Statement - 2
Answer : A

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