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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 479 · 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 40 must be multiplied to get a perfect cube?
  2. 2.What is ∛216? =
  3. 3.What is the smallest whole number by which 2 must be divided to get a perfect cube?
  4. 4.A cube has a volume of 4096 cubic cm. How long is each edge (in cm)?
  5. 5.A big cube of edge 4 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  6. 6.What is ∛125? =
  7. 7.What is 7³? =
  8. 8.A cube has a volume of 3375 cubic cm. How long is each edge (in cm)?
  9. 9.A big cube of edge 12 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  10. 10.What is 20³? =
  11. 11.What is the smallest whole number by which 32 must be multiplied to get a perfect cube?
  12. 12.What is the smallest whole number by which 875 must be divided to get a perfect cube?
  13. 13.A cube has a volume of 1331 cubic cm. How long is each edge (in cm)?
  14. 14.A big cube of edge 10 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  15. 15.A big cube of edge 6 cm is cut into small cubes of edge 2 cm. How many small cubes are there?
  16. 16.What is ∛15625? =
  17. 17.What is the smallest whole number by which 432 must be divided to get a perfect cube?
  18. 18.What is ∛3375? =
  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 ∛9261? =
  21. 21.What is 17³? =
  22. 22.What is the smallest whole number by which 54 must be divided to get a perfect cube?
  23. 23.A cube has a volume of 64 cubic cm. How long is each edge (in cm)?
  24. 24.What is ∛512? =
  25. 25.A cube has a volume of 1000 cubic cm. How long is each edge (in cm)?
  26. 26.What is the smallest whole number by which 448 must be multiplied to get a perfect cube?
  27. 27.What is ∛4913? =
  28. 28.What is 8³? =
  29. 29.Which of these is a perfect cube? (a) 240 (b) 216 (c) 241
  30. 30.What is ∛4096? =
  31. 31.What is ∛8? =
  32. 32.What is the smallest whole number by which 108 must be multiplied to get a perfect cube?
  33. 33.A big cube of edge 5 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  34. 34.Which of these is a perfect cube? (a) 747 (b) 729 (c) 824
  35. 35.A big cube of edge 3 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  36. 36.A cube has a volume of 8000 cubic cm. How long is each edge (in cm)?
  37. 37.What is 11³? =
  38. 38.What is 12³? =
  39. 39.A big cube of edge 2 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  40. 40.Which of these is a perfect cube? (a) 157 (b) 190 (c) 125

Answer key

  1. 25
  2. 6
  3. 2
  4. 16
  5. 8
  6. 5
  7. 343
  8. 15
  9. 27
  10. 8000
  11. 2
  12. 7
  13. 11
  14. 125
  15. 27
  16. 25
  17. 2
  18. 15
  19. 216
  20. 21
  21. 4913
  22. 2
  23. 4
  24. 8
  25. 10
  26. 49
  27. 17
  28. 512
  29. 216
  30. 16
  31. 2
  32. 2
  33. 125
  34. 729
  35. 27
  36. 20
  37. 1331
  38. 1728
  39. 8
  40. 125

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