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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 311 · 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.A big cube of edge 8 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  3. 3.A big cube of edge 6 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  4. 4.A cube has a volume of 216 cubic cm. How long is each edge (in cm)?
  5. 5.A cube has a volume of 343 cubic cm. How long is each edge (in cm)?
  6. 6.A big cube of edge 20 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  7. 7.A big cube of edge 12 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  8. 8.Which of these is a perfect cube? (a) 827 (b) 798 (c) 729
  9. 9.What is ∛343? =
  10. 10.Which of these is a perfect cube? (a) 64 (b) 100 (c) 111
  11. 11.Which of these is a perfect cube? (a) 1287 (b) 1004 (c) 1000
  12. 12.What is the smallest whole number by which 5400 must be divided to get a perfect cube?
  13. 13.What is ∛6859? =
  14. 14.What is the smallest whole number by which 72 must be multiplied to get a perfect cube?
  15. 15.What is 7³? =
  16. 16.What is the smallest whole number by which 56 must be divided to get a perfect cube?
  17. 17.What is ∛2744? =
  18. 18.What is the smallest whole number by which 392 must be multiplied to get a perfect cube?
  19. 19.What is the smallest whole number by which 2 must be divided to get a perfect cube?
  20. 20.Which of these is a perfect cube? (a) 1846 (b) 1728 (c) 2073
  21. 21.What is the smallest whole number by which 128 must be multiplied to get a perfect cube?
  22. 22.What is 8³? =
  23. 23.What is 5³? =
  24. 24.A cube has a volume of 5832 cubic cm. How long is each edge (in cm)?
  25. 25.What is the smallest whole number by which 1600 must be multiplied to get a perfect cube?
  26. 26.A cube has a volume of 6859 cubic cm. How long is each edge (in cm)?
  27. 27.What is 10³? =
  28. 28.What is the smallest whole number by which 1080 must be divided to get a perfect cube?
  29. 29.What is 9³? =
  30. 30.What is the smallest whole number by which 500 must be divided to get a perfect cube?
  31. 31.A big cube of edge 9 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  32. 32.What is ∛2197? =
  33. 33.What is 6³? =
  34. 34.Which of these is a perfect cube? (a) 381 (b) 456 (c) 343
  35. 35.What is the smallest whole number by which 10584 must be multiplied to get a perfect cube?
  36. 36.What is 13³? =
  37. 37.What is 15³? =
  38. 38.A cube has a volume of 8 cubic cm. How long is each edge (in cm)?
  39. 39.What is the smallest whole number by which 81 must be divided to get a perfect cube?
  40. 40.A cube has a volume of 2197 cubic cm. How long is each edge (in cm)?

Answer key

  1. 2
  2. 8
  3. 216
  4. 6
  5. 7
  6. 125
  7. 27
  8. 729
  9. 7
  10. 64
  11. 1000
  12. 25
  13. 19
  14. 3
  15. 343
  16. 7
  17. 14
  18. 7
  19. 2
  20. 1728
  21. 4
  22. 512
  23. 125
  24. 18
  25. 5
  26. 19
  27. 1000
  28. 5
  29. 729
  30. 4
  31. 27
  32. 13
  33. 216
  34. 343
  35. 7
  36. 2197
  37. 3375
  38. 2
  39. 3
  40. 13

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