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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 659 · 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 250 must be multiplied to get a perfect cube?
  2. 2.A cube has a volume of 125 cubic cm. How long is each edge (in cm)?
  3. 3.What is ∛729? =
  4. 4.A big cube of edge 6 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  5. 5.Which of these is a perfect cube? (a) 928 (b) 756 (c) 729
  6. 6.What is ∛125? =
  7. 7.What is ∛2744? =
  8. 8.What is 7³? =
  9. 9.A cube has a volume of 3375 cubic cm. How long is each edge (in cm)?
  10. 10.Which of these is a perfect cube? (a) 216 (b) 314 (c) 246
  11. 11.What is 20³? =
  12. 12.A cube has a volume of 2744 cubic cm. How long is each edge (in cm)?
  13. 13.A cube has a volume of 1331 cubic cm. How long is each edge (in cm)?
  14. 14.A cube has a volume of 729 cubic cm. How long is each edge (in cm)?
  15. 15.A cube has a volume of 216 cubic cm. How long is each edge (in cm)?
  16. 16.A big cube of edge 3 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  17. 17.What is 12³? =
  18. 18.A big cube of edge 24 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  19. 19.What is the smallest whole number by which 6125 must be multiplied to get a perfect cube?
  20. 20.A big cube of edge 12 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  21. 21.What is the smallest whole number by which 375 must be divided to get a perfect cube?
  22. 22.A big cube of edge 2 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  23. 23.A big cube of edge 8 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  24. 24.What is 3³? =
  25. 25.What is 14³? =
  26. 26.What is ∛216? =
  27. 27.Which of these is a perfect cube? (a) 94 (b) 77 (c) 64
  28. 28.A cube has a volume of 27 cubic cm. How long is each edge (in cm)?
  29. 29.Which of these is a perfect cube? (a) 37 (b) 27 (c) 30
  30. 30.What is 9³? =
  31. 31.A big cube of edge 6 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  32. 32.A big cube of edge 8 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  33. 33.What is ∛6859? =
  34. 34.What is ∛1331? =
  35. 35.What is ∛512? =
  36. 36.What is the smallest whole number by which 7 must be multiplied to get a perfect cube?
  37. 37.A cube has a volume of 1728 cubic cm. How long is each edge (in cm)?
  38. 38.What is the smallest whole number by which 32 must be divided to get a perfect cube?
  39. 39.What is the smallest whole number by which 49 must be multiplied to get a perfect cube?
  40. 40.A cube has a volume of 512 cubic cm. How long is each edge (in cm)?

Answer key

  1. 4
  2. 5
  3. 9
  4. 27
  5. 729
  6. 5
  7. 14
  8. 343
  9. 15
  10. 216
  11. 8000
  12. 14
  13. 11
  14. 9
  15. 6
  16. 27
  17. 1728
  18. 216
  19. 7
  20. 64
  21. 3
  22. 8
  23. 64
  24. 27
  25. 2744
  26. 6
  27. 64
  28. 3
  29. 27
  30. 729
  31. 216
  32. 8
  33. 19
  34. 11
  35. 8
  36. 49
  37. 12
  38. 4
  39. 7
  40. 8

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