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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 690 · 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.A big cube of edge 20 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  2. 2.What is ∛4913? =
  3. 3.A big cube of edge 12 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  4. 4.A cube has a volume of 6859 cubic cm. How long is each edge (in cm)?
  5. 5.What is ∛216? =
  6. 6.What is ∛1331? =
  7. 7.What is 3³? =
  8. 8.What is ∛10648? =
  9. 9.Which of these is a perfect cube? (a) 2259 (b) 2197 (c) 2502
  10. 10.What is the smallest whole number by which 250 must be multiplied to get a perfect cube?
  11. 11.What is the smallest whole number by which 9 must be divided to get a perfect cube?
  12. 12.A cube has a volume of 4913 cubic cm. How long is each edge (in cm)?
  13. 13.A cube has a volume of 1728 cubic cm. How long is each edge (in cm)?
  14. 14.A cube has a volume of 1000 cubic cm. How long is each edge (in cm)?
  15. 15.A big cube of edge 15 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  16. 16.A cube has a volume of 8000 cubic cm. How long is each edge (in cm)?
  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.What is ∛512? =
  19. 19.What is 2³? =
  20. 20.A big cube of edge 2 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  21. 21.A big cube of edge 8 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  22. 22.What is 18³? =
  23. 23.What is the smallest whole number by which 128 must be multiplied to get a perfect cube?
  24. 24.A cube has a volume of 4096 cubic cm. How long is each edge (in cm)?
  25. 25.Which of these is a perfect cube? (a) 98 (b) 68 (c) 64
  26. 26.What is 13³? =
  27. 27.Which of these is a perfect cube? (a) 1728 (b) 2131 (c) 2114
  28. 28.What is 16³? =
  29. 29.What is the smallest whole number by which 1323 must be multiplied to get a perfect cube?
  30. 30.What is 5³? =
  31. 31.What is the smallest whole number by which 648 must be divided to get a perfect cube?
  32. 32.What is ∛1728? =
  33. 33.A big cube of edge 4 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  34. 34.What is ∛2744? =
  35. 35.What is ∛1000? =
  36. 36.What is 17³? =
  37. 37.A cube has a volume of 1331 cubic cm. How long is each edge (in cm)?
  38. 38.A big cube of edge 5 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  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.What is the smallest whole number by which 256 must be divided to get a perfect cube?

Answer key

  1. 125
  2. 17
  3. 27
  4. 19
  5. 6
  6. 11
  7. 27
  8. 22
  9. 2197
  10. 4
  11. 9
  12. 17
  13. 12
  14. 10
  15. 125
  16. 20
  17. 27
  18. 8
  19. 8
  20. 8
  21. 64
  22. 5832
  23. 4
  24. 16
  25. 64
  26. 2197
  27. 1728
  28. 4096
  29. 7
  30. 125
  31. 3
  32. 12
  33. 64
  34. 14
  35. 10
  36. 4913
  37. 11
  38. 125
  39. 27
  40. 4

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