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Class 8 Maths Worksheet: Cubes and Cube Roots

Maths worksheets lesson 59: Cubes and cube roots · Set 648 · 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 1512 must be divided to get a perfect cube?
  2. 2.What is the smallest whole number by which 32 must be multiplied to get a perfect cube?
  3. 3.What is the smallest whole number by which 375 must be multiplied to get a perfect cube?
  4. 4.What is ∛8000? =
  5. 5.What is the smallest whole number by which 500 must be divided to get a perfect cube?
  6. 6.What is ∛1000? =
  7. 7.A cube has a volume of 1331 cubic cm. How long is each edge (in cm)?
  8. 8.A cube has a volume of 1000 cubic cm. How long is each edge (in cm)?
  9. 9.A cube has a volume of 4096 cubic cm. How long is each edge (in cm)?
  10. 10.What is 8³? =
  11. 11.A big cube of edge 6 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  12. 12.What is the smallest whole number by which 392 must be multiplied to get a perfect cube?
  13. 13.A cube has a volume of 8 cubic cm. How long is each edge (in cm)?
  14. 14.What is 17³? =
  15. 15.A big cube of edge 2 cm is cut into small cubes of edge 1 cm. How many small cubes are there?
  16. 16.What is ∛4096? =
  17. 17.A cube has a volume of 343 cubic cm. How long is each edge (in cm)?
  18. 18.What is 11³? =
  19. 19.What is 6³? =
  20. 20.Which of these is a perfect cube? (a) 165 (b) 176 (c) 125
  21. 21.What is the smallest whole number by which 1323 must be multiplied to get a perfect cube?
  22. 22.What is 3³? =
  23. 23.Which of these is a perfect cube? (a) 343 (b) 394 (c) 367
  24. 24.What is ∛6859? =
  25. 25.What is 16³? =
  26. 26.What is ∛1728? =
  27. 27.What is 7³? =
  28. 28.A big cube of edge 15 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  29. 29.What is the smallest whole number by which 648 must be multiplied to get a perfect cube?
  30. 30.A cube has a volume of 1728 cubic cm. How long is each edge (in cm)?
  31. 31.A cube has a volume of 3375 cubic cm. How long is each edge (in cm)?
  32. 32.What is the smallest whole number by which 25 must be divided to get a perfect cube?
  33. 33.Which of these is a perfect cube? (a) 737 (b) 729 (c) 891
  34. 34.What is ∛512? =
  35. 35.What is ∛1331? =
  36. 36.What is the smallest whole number by which 54 must be multiplied to get a perfect cube?
  37. 37.A big cube of edge 12 cm is cut into small cubes of edge 3 cm. How many small cubes are there?
  38. 38.A big cube of edge 20 cm is cut into small cubes of edge 4 cm. How many small cubes are there?
  39. 39.What is ∛2744? =
  40. 40.A cube has a volume of 729 cubic cm. How long is each edge (in cm)?

Answer key

  1. 7
  2. 2
  3. 9
  4. 20
  5. 4
  6. 10
  7. 11
  8. 10
  9. 16
  10. 512
  11. 8
  12. 7
  13. 2
  14. 4913
  15. 8
  16. 16
  17. 7
  18. 1331
  19. 216
  20. 125
  21. 7
  22. 27
  23. 343
  24. 19
  25. 4096
  26. 12
  27. 343
  28. 125
  29. 9
  30. 12
  31. 15
  32. 25
  33. 729
  34. 8
  35. 11
  36. 4
  37. 64
  38. 125
  39. 14
  40. 9

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