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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 20 · 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 81 must be multiplied to get a perfect cube?
  2. 2.What is 13³? =
  3. 3.What is ∛216? =
  4. 4.A big cube of edge 24 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  5. 5.Which of these is a perfect cube? (a) 64 (b) 98 (c) 87
  6. 6.A big cube of edge 9 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  7. 7.A cube has a volume of 1728 cubic cm. How long is each edge (in cm)?
  8. 8.A big cube of edge 6 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  9. 9.Which of these is a perfect cube? (a) 192 (b) 182 (c) 125
  10. 10.What is the smallest whole number by which 392 must be divided to get a perfect cube?
  11. 11.What is the smallest whole number by which 128 must be divided to get a perfect cube?
  12. 12.Which of these is a perfect cube? (a) 29 (b) 27 (c) 53
  13. 13.What is the smallest whole number by which 243 must be multiplied to get a perfect cube?
  14. 14.What is ∛125? =
  15. 15.What is the smallest whole number by which 10584 must be multiplied to get a perfect cube?
  16. 16.A big cube of edge 5 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  17. 17.What is ∛2197? =
  18. 18.What is 2³? =
  19. 19.A cube has a volume of 3375 cubic cm. How long is each edge (in cm)?
  20. 20.What is ∛8000? =
  21. 21.Which of these is a perfect cube? (a) 377 (b) 343 (c) 435
  22. 22.What is the smallest whole number by which 875 must be divided to get a perfect cube?
  23. 23.What is ∛343? =
  24. 24.What is the smallest whole number by which 32 must be divided to get a perfect cube?
  25. 25.Which of these is a perfect cube? (a) 1057 (b) 1140 (c) 1000
  26. 26.A cube has a volume of 2744 cubic cm. How long is each edge (in cm)?
  27. 27.A cube has a volume of 4913 cubic cm. How long is each edge (in cm)?
  28. 28.What is 20³? =
  29. 29.A big cube of edge 18 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  30. 30.A cube has a volume of 4096 cubic cm. How long is each edge (in cm)?
  31. 31.What is the smallest whole number by which 3125 must be multiplied to get a perfect cube?
  32. 32.A big cube of edge 3 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  33. 33.What is ∛2744? =
  34. 34.What is 6³? =
  35. 35.What is the smallest whole number by which 32 must be multiplied to get a perfect cube?
  36. 36.What is 4³? =
  37. 37.A big cube of edge 8 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  38. 38.What is 3³? =
  39. 39.What is 8³? =
  40. 40.What is the smallest whole number by which 189 must be multiplied to get a perfect cube?

Answer key

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

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