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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 484 · 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 7 must be multiplied to get a perfect cube?
  2. 2.What is ∛13824? =
  3. 3.What is ∛1331? =
  4. 4.What is the smallest whole number by which 500 must be divided to get a perfect cube?
  5. 5.A cube has a volume of 4096 cubic cm. How long is each edge (in cm)?
  6. 6.What is the smallest whole number by which 1512 must be multiplied to get a perfect cube?
  7. 7.What is 8³? =
  8. 8.Which of these is a perfect cube? (a) 3477 (b) 3375 (c) 3904
  9. 9.What is the smallest whole number by which 108 must be multiplied to get a perfect cube?
  10. 10.A cube has a volume of 3375 cubic cm. How long is each edge (in cm)?
  11. 11.A big cube of edge 2 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  12. 12.What is 9³? =
  13. 13.A cube has a volume of 125 cubic cm. How long is each edge (in cm)?
  14. 14.What is ∛343? =
  15. 15.A big cube of edge 3 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  16. 16.What is ∛2744? =
  17. 17.A big cube of edge 24 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  18. 18.What is the smallest whole number by which 49 must be multiplied to get a perfect cube?
  19. 19.What is 7³? =
  20. 20.A big cube of edge 16 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  21. 21.What is ∛729? =
  22. 22.What is the smallest whole number by which 864 must be multiplied to get a perfect cube?
  23. 23.Which of these is a perfect cube? (a) 729 (b) 950 (c) 957
  24. 24.What is ∛3375? =
  25. 25.What is ∛216? =
  26. 26.Which of these is a perfect cube? (a) 36 (b) 30 (c) 27
  27. 27.A big cube of edge 20 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  28. 28.A cube has a volume of 729 cubic cm. How long is each edge (in cm)?
  29. 29.A big cube of edge 6 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  30. 30.What is 3³? =
  31. 31.Which of these is a perfect cube? (a) 2594 (b) 2409 (c) 2197
  32. 32.A big cube of edge 12 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  33. 33.What is the smallest whole number by which 54 must be multiplied to get a perfect cube?
  34. 34.What is 2³? =
  35. 35.A big cube of edge 10 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  36. 36.What is ∛512? =
  37. 37.What is ∛4096? =
  38. 38.A big cube of edge 6 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  39. 39.What is ∛8? =
  40. 40.What is the smallest whole number by which 3 must be multiplied to get a perfect cube?

Answer key

  1. 49
  2. 24
  3. 11
  4. 4
  5. 16
  6. 49
  7. 512
  8. 3375
  9. 2
  10. 15
  11. 8
  12. 729
  13. 5
  14. 7
  15. 27
  16. 14
  17. 216
  18. 7
  19. 343
  20. 64
  21. 9
  22. 2
  23. 729
  24. 15
  25. 6
  26. 27
  27. 125
  28. 9
  29. 8
  30. 27
  31. 2197
  32. 27
  33. 4
  34. 8
  35. 125
  36. 8
  37. 16
  38. 216
  39. 2
  40. 9

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