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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 90 · 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 56 must be multiplied to get a perfect cube?
  2. 2.What is the smallest whole number by which 576 must be multiplied to get a perfect cube?
  3. 3.Which of these is a perfect cube? (a) 1161 (b) 1094 (c) 1000
  4. 4.What is ∛10648? =
  5. 5.A cube has a volume of 125 cubic cm. How long is each edge (in cm)?
  6. 6.A big cube of edge 18 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  7. 7.What is 3³? =
  8. 8.A big cube of edge 20 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  9. 9.What is 4³? =
  10. 10.A big cube of edge 6 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  11. 11.What is the smallest whole number by which 432 must be multiplied to get a perfect cube?
  12. 12.What is the smallest whole number by which 1080 must be multiplied to get a perfect cube?
  13. 13.What is the smallest whole number by which 3 must be divided to get a perfect cube?
  14. 14.A cube has a volume of 729 cubic cm. How long is each edge (in cm)?
  15. 15.What is ∛12167? =
  16. 16.What is the smallest whole number by which 320 must be multiplied to get a perfect cube?
  17. 17.A big cube of edge 3 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  18. 18.A big cube of edge 4 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  19. 19.What is 12³? =
  20. 20.What is 8³? =
  21. 21.A cube has a volume of 2197 cubic cm. How long is each edge (in cm)?
  22. 22.What is 7³? =
  23. 23.A cube has a volume of 6859 cubic cm. How long is each edge (in cm)?
  24. 24.What is 14³? =
  25. 25.A big cube of edge 4 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  26. 26.What is ∛125? =
  27. 27.What is the smallest whole number by which 375 must be multiplied to get a perfect cube?
  28. 28.A cube has a volume of 2744 cubic cm. How long is each edge (in cm)?
  29. 29.What is 20³? =
  30. 30.What is ∛3375? =
  31. 31.A big cube of edge 24 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  32. 32.What is ∛6859? =
  33. 33.What is ∛343? =
  34. 34.Which of these is a perfect cube? (a) 2479 (b) 2611 (c) 2197
  35. 35.A big cube of edge 6 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  36. 36.What is the smallest whole number by which 54 must be divided to get a perfect cube?
  37. 37.What is the smallest whole number by which 72 must be multiplied to get a perfect cube?
  38. 38.A cube has a volume of 216 cubic cm. How long is each edge (in cm)?
  39. 39.A cube has a volume of 64 cubic cm. How long is each edge (in cm)?
  40. 40.A cube has a volume of 343 cubic cm. How long is each edge (in cm)?

Answer key

  1. 49
  2. 3
  3. 1000
  4. 22
  5. 5
  6. 216
  7. 27
  8. 125
  9. 64
  10. 27
  11. 4
  12. 25
  13. 3
  14. 9
  15. 23
  16. 25
  17. 27
  18. 64
  19. 1728
  20. 512
  21. 13
  22. 343
  23. 19
  24. 2744
  25. 8
  26. 5
  27. 9
  28. 14
  29. 8000
  30. 15
  31. 216
  32. 19
  33. 7
  34. 2197
  35. 216
  36. 2
  37. 3
  38. 6
  39. 4
  40. 7

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