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Cubes and Cube Roots

Question paper, Set 10

  • Set 10 of 10
  • 20 questions
  • 50 marks
  • 1 hour 30 minutes

Download the PDF (with key sheet and solutions, 74.5 KB)

Work each question on paper first, then open its answer and solution to check your work.

  1. Write t×t×tt \times t \times t in power form.
    1 mark
    Answer and solution

    t×t×t=t3t \times t \times t = t^3

    Read it as 't cubed'.

    Answer: t3t^3

  2. Write m×m×m×z×z×zm \times m \times m \times z \times z \times z in power form.
    2 marks
    Answer and solution

    m×m×m=m3m \times m \times m = m^3

    z×z×z=z3z \times z \times z = z^3

    ∴m×m×m×z×z×z=m3×z3\therefore m \times m \times m \times z \times z \times z = m^3 \times z^3

    Answer: m3×z3m^3 \times z^3

  3. Find the value of 232^3.
    1 mark
    Answer and solution

    23=2×2×22^3 = 2 \times 2 \times 2

    =4×2=8= 4 \times 2 = 8

    Answer: 88

  4. Is 50 the cube of a whole number? Use the table of cubes.
    2 marks
    Answer and solution

    From the table: 33=273^3 = 27 and 43=644^3 = 64.

    27<50<6427 < 50 < 64, and no whole number lies between 3 and 4.

    So 50 is not a cube.

    Answer: No, it lies between 33=273^3 = 27 and 43=644^3 = 64

  5. A cube-shaped stack of dice has 5 dice along each edge. (i) How many dice are in the top layer? (ii) How many dice are there in the whole stack?
    3 marks
    Answer and solution

    (i) One layer has 5 rows of 5: 5×5=255 \times 5 = 25

    (ii) There are 5 layers: 25×5=12525 \times 5 = 125

    So there are 53=1255^3 = 125 dice.

    Answer: (i) 2525 (ii) 125125

  6. Find 19319^3 by first finding 19×1919 \times 19.
    2 marks
    Answer and solution

    19×19=36119 \times 19 = 361

    193=361×19=685919^3 = 361 \times 19 = 6859

    Answer: 68596859

  7. Three cube-shaped piles of building blocks have 14, 15 and 40 blocks along each edge. How many blocks does each pile have?
    5 marks
    Answer and solution

    Edge 14: 14×14=19614 \times 14 = 196, 196×14=2744196 \times 14 = 2744

    Edge 15: 15×15=22515 \times 15 = 225, 225×15=3375225 \times 15 = 3375

    Edge 40: 40×40=160040 \times 40 = 1600, 1600×40=640001600 \times 40 = 64000

    Answer: 27442744, 33753375, 6400064000 blocks

  8. Without working it out, say whether (−11)3(-11)^3 is positive or negative. Give the reason.
    1 mark
    Answer and solution

    (−11)3=−113(-11)^3 = -11^3

    The cube of a negative number is negative.

    Answer: Negative

  9. Ravi wrote (−7)3=343(-7)^3 = 343. Is he right? Write the correct value.
    2 marks
    Answer and solution

    (−7)3=(−7)×(−7)×(−7)(-7)^3 = (-7) \times (-7) \times (-7)

    =49×(−7)=−343= 49 \times (-7) = -343

    A negative number multiplied 3 times gives a negative answer, so Ravi is wrong.

    Answer: No. (−7)3=−343(-7)^3 = -343

  10. Find (−6)3(-6)^3 and 636^3. Which of the two is bigger, and why?
    3 marks
    Answer and solution

    63=6×6×6=2166^3 = 6 \times 6 \times 6 = 216

    (−6)3=(−6)×(−6)×(−6)=−216(-6)^3 = (-6) \times (-6) \times (-6) = -216

    216216 is positive and −216-216 is negative, so 636^3 is bigger.

    Answer: 63=2166^3 = 216 is bigger than (−6)3=−216(-6)^3 = -216

  11. Find 83+838^3 + 8^3.
    1 mark
    Answer and solution

    83+83=512+5128^3 + 8^3 = 512 + 512

    =1024= 1024

    Answer: 10241024

  12. Find the sum of the cubes of all the even numbers from 2 to 10.
    5 marks
    Answer and solution

    23+43+63+83+103=8+64+216+512+10002^3 + 4^3 + 6^3 + 8^3 + 10^3 = 8 + 64 + 216 + 512 + 1000

    =1800= 1800

    Answer: 18001800

  13. Find the value of (−25)3+253(-25)^3 + 25^3.
    1 mark
    Answer and solution

    (−25)3=−253(-25)^3 = -25^3

    (−25)3+253=253−253=0(-25)^3 + 25^3 = 25^3 - 25^3 = 0

    Answer: 00

  14. Find the value of x3+(−y)3x^3 + (-y)^3 when x=4x = 4 and y=7y = 7.
    2 marks
    Answer and solution

    x3+(−y)3=43+(−7)3x^3 + (-y)^3 = 4^3 + (-7)^3

    43+(−7)3=64+(−343)4^3 + (-7)^3 = 64 + (-343)

    =64−343= 64 - 343

    =−279= -279

    Answer: −279-279

  15. Ravi found 23−83=5042^3 - 8^3 = 504. Is he right? Find the correct answer.
    2 marks
    Answer and solution

    23−83=8−5122^3 - 8^3 = 8 - 512

    We take away the bigger number 512 from the smaller number 8, so the answer is negative.

    8−512=−5048 - 512 = -504

    Ravi subtracted the other way round; the correct answer is −504-504.

    Answer: No. 23−83=−5042^3 - 8^3 = -504

  16. Find 133−10313^3 - 10^3.
    3 marks
    Answer and solution

    133=169×13=219713^3 = 169 \times 13 = 2197

    133−103=2197−100013^3 - 10^3 = 2197 - 1000

    =1197= 1197

    Answer: 11971197

  17. Simplify 103−33−9310^3 - 3^3 - 9^3.
    5 marks
    Answer and solution

    103−33−93=1000−27−72910^3 - 3^3 - 9^3 = 1000 - 27 - 729

    =244= 244

    Answer: 244244

  18. Simplify n3−(−n)3n^3 - (-n)^3.
    1 mark
    Answer and solution

    (−n)3=−n3(-n)^3 = -n^3

    n3−(−n3)=n3+n3=2n3n^3 - (-n^3) = n^3 + n^3 = 2n^3

    Answer: 2n32n^3

  19. Find the value of (−2)3−(−5)3(-2)^3 - (-5)^3.
    3 marks
    Answer and solution

    (−2)3−(−5)3=−8−(−125)(-2)^3 - (-5)^3 = -8 - (-125)

    =−8+125= -8 + 125

    =117= 117

    Answer: 117117

  20. Find 103−93+83−7310^3 - 9^3 + 8^3 - 7^3.
    5 marks
    Answer and solution

    103−93+83−73=1000−729+512−34310^3 - 9^3 + 8^3 - 7^3 = 1000 - 729 + 512 - 343

    =440= 440

    Answer: 440440