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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 254 · 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 19³? =
  2. 2.A big cube of edge 6 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  3. 3.Which of these is a perfect cube? (a) 860 (b) 746 (c) 729
  4. 4.A big cube of edge 18 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  5. 5.Which of these is a perfect cube? (a) 2876 (b) 2744 (c) 3272
  6. 6.What is 7³? =
  7. 7.A big cube of edge 2 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  8. 8.What is the smallest whole number by which 56 must be multiplied to get a perfect cube?
  9. 9.What is the smallest whole number by which 32 must be multiplied to get a perfect cube?
  10. 10.What is 4³? =
  11. 11.What is 16³? =
  12. 12.What is 3³? =
  13. 13.What is ∛15625? =
  14. 14.Which of these is a perfect cube? (a) 64 (b) 83 (c) 65
  15. 15.A big cube of edge 8 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  16. 16.A cube has a volume of 512 cubic cm. How long is each edge (in cm)?
  17. 17.What is the smallest whole number by which 648 must be divided to get a perfect cube?
  18. 18.A cube has a volume of 343 cubic cm. How long is each edge (in cm)?
  19. 19.A big cube of edge 4 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  20. 20.A big cube of edge 12 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  21. 21.A cube has a volume of 64 cubic cm. How long is each edge (in cm)?
  22. 22.What is the smallest whole number by which 40 must be multiplied to get a perfect cube?
  23. 23.A cube has a volume of 1000 cubic cm. How long is each edge (in cm)?
  24. 24.What is ∛1728? =
  25. 25.What is the smallest whole number by which 25 must be multiplied to get a perfect cube?
  26. 26.What is the smallest whole number by which 24 must be divided to get a perfect cube?
  27. 27.What is ∛8000? =
  28. 28.What is the smallest whole number by which 16 must be multiplied to get a perfect cube?
  29. 29.A big cube of edge 8 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  30. 30.What is ∛4913? =
  31. 31.A cube has a volume of 1331 cubic cm. How long is each edge (in cm)?
  32. 32.What is ∛12167? =
  33. 33.What is 5³? =
  34. 34.What is 6³? =
  35. 35.A cube has a volume of 1728 cubic cm. How long is each edge (in cm)?
  36. 36.A big cube of edge 5 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  37. 37.A big cube of edge 4 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  38. 38.What is ∛13824? =
  39. 39.What is the smallest whole number by which 243 must be divided to get a perfect cube?
  40. 40.What is the smallest whole number by which 81 must be multiplied to get a perfect cube?

Answer key

  1. 6859
  2. 8
  3. 729
  4. 216
  5. 2744
  6. 343
  7. 8
  8. 49
  9. 2
  10. 64
  11. 4096
  12. 27
  13. 25
  14. 64
  15. 8
  16. 8
  17. 3
  18. 7
  19. 8
  20. 27
  21. 4
  22. 25
  23. 10
  24. 12
  25. 5
  26. 3
  27. 20
  28. 4
  29. 64
  30. 17
  31. 11
  32. 23
  33. 125
  34. 216
  35. 12
  36. 125
  37. 64
  38. 24
  39. 9
  40. 9

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