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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 890 · 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.A big cube of edge 5 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  2. 2.What is the smallest whole number by which 24 must be divided to get a perfect cube?
  3. 3.What is ∛27? =
  4. 4.What is ∛1728? =
  5. 5.Which of these is a perfect cube? (a) 2239 (b) 2486 (c) 2197
  6. 6.A cube has a volume of 2744 cubic cm. How long is each edge (in cm)?
  7. 7.What is 18³? =
  8. 8.What is ∛2744? =
  9. 9.A cube has a volume of 64 cubic cm. How long is each edge (in cm)?
  10. 10.What is ∛15625? =
  11. 11.Which of these is a perfect cube? (a) 799 (b) 810 (c) 729
  12. 12.Which of these is a perfect cube? (a) 1905 (b) 1728 (c) 2005
  13. 13.A big cube of edge 18 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  14. 14.A big cube of edge 16 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  15. 15.A big cube of edge 2 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  16. 16.What is the smallest whole number by which 189 must be divided to get a perfect cube?
  17. 17.What is ∛125? =
  18. 18.What is the smallest whole number by which 72 must be divided to get a perfect cube?
  19. 19.What is 13³? =
  20. 20.What is the smallest whole number by which 16 must be multiplied to get a perfect cube?
  21. 21.A cube has a volume of 512 cubic cm. How long is each edge (in cm)?
  22. 22.A big cube of edge 6 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  23. 23.What is ∛13824? =
  24. 24.What is 12³? =
  25. 25.Which of these is a perfect cube? (a) 98 (b) 112 (c) 64
  26. 26.A big cube of edge 3 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  27. 27.What is ∛12167? =
  28. 28.A cube has a volume of 6859 cubic cm. How long is each edge (in cm)?
  29. 29.What is ∛9261? =
  30. 30.A cube has a volume of 4913 cubic cm. How long is each edge (in cm)?
  31. 31.What is the smallest whole number by which 576 must be multiplied to get a perfect cube?
  32. 32.What is 4³? =
  33. 33.What is ∛3375? =
  34. 34.What is 17³? =
  35. 35.What is 5³? =
  36. 36.What is the smallest whole number by which 16 must be divided to get a perfect cube?
  37. 37.Which of these is a perfect cube? (a) 679 (b) 512 (c) 609
  38. 38.What is the smallest whole number by which 256 must be divided to get a perfect cube?
  39. 39.A big cube of edge 4 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  40. 40.Which of these is a perfect cube? (a) 3470 (b) 3375 (c) 4024

Answer key

  1. 125
  2. 3
  3. 3
  4. 12
  5. 2197
  6. 14
  7. 5832
  8. 14
  9. 4
  10. 25
  11. 729
  12. 1728
  13. 216
  14. 64
  15. 8
  16. 7
  17. 5
  18. 9
  19. 2197
  20. 4
  21. 8
  22. 216
  23. 24
  24. 1728
  25. 64
  26. 27
  27. 23
  28. 19
  29. 21
  30. 17
  31. 3
  32. 64
  33. 15
  34. 4913
  35. 125
  36. 2
  37. 512
  38. 4
  39. 64
  40. 3375

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