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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 436 · 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 1944 must be multiplied to get a perfect cube?
  2. 2.What is the smallest whole number by which 875 must be multiplied to get a perfect cube?
  3. 3.What is 5³? =
  4. 4.What is ∛12167? =
  5. 5.What is 9³? =
  6. 6.A cube has a volume of 8 cubic cm. How long is each edge (in cm)?
  7. 7.Which of these is a perfect cube? (a) 179 (b) 125 (c) 131
  8. 8.A cube has a volume of 6859 cubic cm. How long is each edge (in cm)?
  9. 9.Which of these is a perfect cube? (a) 1331 (b) 1429 (c) 1436
  10. 10.A cube has a volume of 216 cubic cm. How long is each edge (in cm)?
  11. 11.What is ∛9261? =
  12. 12.What is ∛2744? =
  13. 13.What is the smallest whole number by which 9 must be divided to get a perfect cube?
  14. 14.A big cube of edge 6 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  15. 15.What is ∛8? =
  16. 16.What is ∛2197? =
  17. 17.A big cube of edge 5 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  18. 18.What is the smallest whole number by which 1125 must be multiplied to get a perfect cube?
  19. 19.A big cube of edge 12 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  20. 20.What is ∛64? =
  21. 21.What is the smallest whole number by which 256 must be multiplied to get a perfect cube?
  22. 22.What is ∛5832? =
  23. 23.A big cube of edge 20 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  24. 24.What is ∛8000? =
  25. 25.A big cube of edge 16 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  26. 26.What is 6³? =
  27. 27.A cube has a volume of 1728 cubic cm. How long is each edge (in cm)?
  28. 28.A cube has a volume of 4913 cubic cm. How long is each edge (in cm)?
  29. 29.A cube has a volume of 2197 cubic cm. How long is each edge (in cm)?
  30. 30.A cube has a volume of 125 cubic cm. How long is each edge (in cm)?
  31. 31.What is ∛27? =
  32. 32.A big cube of edge 8 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  33. 33.Which of these is a perfect cube? (a) 83 (b) 72 (c) 64
  34. 34.What is 2³? =
  35. 35.What is ∛1728? =
  36. 36.What is 11³? =
  37. 37.What is the smallest whole number by which 135 must be divided to get a perfect cube?
  38. 38.What is the smallest whole number by which 5 must be divided to get a perfect cube?
  39. 39.A big cube of edge 9 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  40. 40.A big cube of edge 4 cm is cut into small cubes of edge 1 cm. How many small cubes are there?

Answer key

  1. 3
  2. 49
  3. 125
  4. 23
  5. 729
  6. 2
  7. 125
  8. 19
  9. 1331
  10. 6
  11. 21
  12. 14
  13. 9
  14. 216
  15. 2
  16. 13
  17. 125
  18. 3
  19. 216
  20. 4
  21. 2
  22. 18
  23. 125
  24. 20
  25. 64
  26. 216
  27. 12
  28. 17
  29. 13
  30. 5
  31. 3
  32. 64
  33. 64
  34. 8
  35. 12
  36. 1331
  37. 5
  38. 5
  39. 27
  40. 64

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