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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 162 · 40 sums
TalentJR

The method (Threes make cubes): Cube: n × n × n. Cube root: the number that, used three times, gives the cube. Units digits: 1→1, 2→8, 3→7, 4→4, 5→5, 6→6, 7→3, 8→2, 9→9, 0→0 — use them to guess cube roots. Make a perfect cube: break into primes; multiply by what completes each group of three (or divide by what is left over). A big cube of edge a cut into small cubes of edge b gives (a ÷ b)³ small cubes.

NameDateTime takenScore ___ / 40
  1. 1.What is the smallest whole number by which 3125 must be multiplied to get a perfect cube?
  2. 2.What is ∛10648? =
  3. 3.What is ∛3375? =
  4. 4.What is ∛27? =
  5. 5.A big cube of edge 12 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  6. 6.What is the smallest whole number by which 49 must be divided to get a perfect cube?
  7. 7.What is 5³? =
  8. 8.A cube has a volume of 4913 cubic cm. How long is each edge (in cm)?
  9. 9.What is the smallest whole number by which 864 must be multiplied to get a perfect cube?
  10. 10.What is ∛6859? =
  11. 11.A cube has a volume of 8000 cubic cm. How long is each edge (in cm)?
  12. 12.A big cube of edge 12 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  13. 13.What is the smallest whole number by which 135 must be divided to get a perfect cube?
  14. 14.A cube has a volume of 6859 cubic cm. How long is each edge (in cm)?
  15. 15.What is 19³? =
  16. 16.A cube has a volume of 4096 cubic cm. How long is each edge (in cm)?
  17. 17.What is ∛9261? =
  18. 18.What is ∛343? =
  19. 19.What is 18³? =
  20. 20.What is 16³? =
  21. 21.Which of these is a perfect cube? (a) 99 (b) 101 (c) 64
  22. 22.Which of these is a perfect cube? (a) 2891 (b) 3091 (c) 2744
  23. 23.Which of these is a perfect cube? (a) 4046 (b) 3375 (c) 3753
  24. 24.A cube has a volume of 1331 cubic cm. How long is each edge (in cm)?
  25. 25.What is 7³? =
  26. 26.A cube has a volume of 27 cubic cm. How long is each edge (in cm)?
  27. 27.Which of these is a perfect cube? (a) 701 (b) 681 (c) 512
  28. 28.What is the smallest whole number by which 56 must be divided to get a perfect cube?
  29. 29.What is ∛15625? =
  30. 30.A big cube of edge 6 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  31. 31.What is 8³? =
  32. 32.Which of these is a perfect cube? (a) 2231 (b) 2197 (c) 2637
  33. 33.A cube has a volume of 2197 cubic cm. How long is each edge (in cm)?
  34. 34.A cube has a volume of 8 cubic cm. How long is each edge (in cm)?
  35. 35.What is 14³? =
  36. 36.What is ∛64? =
  37. 37.What is the smallest whole number by which 392 must be divided to get a perfect cube?
  38. 38.What is ∛13824? =
  39. 39.A big cube of edge 20 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  40. 40.What is the smallest whole number by which 189 must be divided to get a perfect cube?

Answer key

  1. 5
  2. 22
  3. 15
  4. 3
  5. 216
  6. 49
  7. 125
  8. 17
  9. 2
  10. 19
  11. 20
  12. 27
  13. 5
  14. 19
  15. 6859
  16. 16
  17. 21
  18. 7
  19. 5832
  20. 4096
  21. 64
  22. 2744
  23. 3375
  24. 11
  25. 343
  26. 3
  27. 512
  28. 7
  29. 25
  30. 8
  31. 512
  32. 2197
  33. 13
  34. 2
  35. 2744
  36. 4
  37. 49
  38. 24
  39. 125
  40. 7

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