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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 158 · 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 500 must be multiplied to get a perfect cube?
  2. 2.What is ∛12167? =
  3. 3.What is the smallest whole number by which 256 must be multiplied to get a perfect cube?
  4. 4.What is ∛4913? =
  5. 5.A cube has a volume of 8000 cubic cm. How long is each edge (in cm)?
  6. 6.A cube has a volume of 1000 cubic cm. How long is each edge (in cm)?
  7. 7.What is 14³? =
  8. 8.What is ∛3375? =
  9. 9.What is ∛64? =
  10. 10.What is the smallest whole number by which 9 must be divided to get a perfect cube?
  11. 11.What is 19³? =
  12. 12.A cube has a volume of 6859 cubic cm. How long is each edge (in cm)?
  13. 13.A cube has a volume of 4096 cubic cm. How long is each edge (in cm)?
  14. 14.What is ∛15625? =
  15. 15.A big cube of edge 12 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  16. 16.A cube has a volume of 5832 cubic cm. How long is each edge (in cm)?
  17. 17.What is the smallest whole number by which 576 must be multiplied to get a perfect cube?
  18. 18.A big cube of edge 3 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  19. 19.What is ∛1000? =
  20. 20.What is ∛2197? =
  21. 21.Which of these is a perfect cube? (a) 309 (b) 216 (c) 245
  22. 22.What is ∛1331? =
  23. 23.Which of these is a perfect cube? (a) 731 (b) 729 (c) 803
  24. 24.A big cube of edge 16 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  25. 25.A big cube of edge 8 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  26. 26.A cube has a volume of 1728 cubic cm. How long is each edge (in cm)?
  27. 27.Which of these is a perfect cube? (a) 85 (b) 84 (c) 64
  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 24 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  30. 30.What is ∛216? =
  31. 31.What is ∛343? =
  32. 32.What is 6³? =
  33. 33.What is 7³? =
  34. 34.What is 5³? =
  35. 35.What is ∛27? =
  36. 36.A cube has a volume of 64 cubic cm. How long is each edge (in cm)?
  37. 37.A big cube of edge 5 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  38. 38.Which of these is a perfect cube? (a) 1331 (b) 1674 (c) 1597
  39. 39.What is ∛6859? =
  40. 40.What is ∛1728? =

Answer key

  1. 2
  2. 23
  3. 2
  4. 17
  5. 20
  6. 10
  7. 2744
  8. 15
  9. 4
  10. 9
  11. 6859
  12. 19
  13. 16
  14. 25
  15. 216
  16. 18
  17. 3
  18. 27
  19. 10
  20. 13
  21. 216
  22. 11
  23. 729
  24. 64
  25. 8
  26. 12
  27. 64
  28. 9
  29. 216
  30. 6
  31. 7
  32. 216
  33. 343
  34. 125
  35. 3
  36. 4
  37. 125
  38. 1331
  39. 19
  40. 12

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