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Cubes and Cube Roots

Question paper, Set 7

  • Set 7 of 10
  • 20 questions
  • 50 marks
  • 1 hour 30 minutes

Download the PDF (with key sheet and solutions, 76.3 KB)

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

  1. Write n3n^3 in words.
    1 mark
    Answer and solution

    n3=n×n×nn^3 = n \times n \times n

    It is read as 'nn power 3' (or) 'nn cubed'.

    Answer: nn power 3 (or) nn cubed

  2. Write b×b×b×c×c×cb \times b \times b \times c \times c \times c using cubes.
    2 marks
    Answer and solution

    b×b×b=b3b \times b \times b = b^3

    c×c×c=c3c \times c \times c = c^3

    ∴b×b×b×c×c×c=b3×c3\therefore b \times b \times b \times c \times c \times c = b^3 \times c^3

    Answer: b3×c3b^3 \times c^3

  3. Write the value of 333^3 from the table of cubes.
    1 mark
    Answer and solution

    33=3×3×33^3 = 3 \times 3 \times 3

    =9×3=27= 9 \times 3 = 27

    Answer: 2727

  4. 600 lies between the cubes of which two consecutive numbers?
    2 marks
    Answer and solution

    From the table: 83=5128^3 = 512 and 93=7299^3 = 729.

    512<600<729512 < 600 < 729

    So 600 lies between 838^3 and 939^3.

    Answer: Between 838^3 and 939^3

  5. Which of these numbers are cubes? Write each cube as the cube of a number: 8, 16, 216, 400, 512.
    3 marks
    Answer and solution

    Check each number with the table of cubes.

    23=82^3 = 8

    63=2166^3 = 216

    83=5128^3 = 512

    The other numbers are not in the table of cubes, so they are not cubes.

    Answer: 8=238 = 2^3, 216=63216 = 6^3, 512=83512 = 8^3

  6. Find the value of 13313^3.
    2 marks
    Answer and solution

    13×13=16913 \times 13 = 169

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

    Answer: 21972197

  7. Asha wrote 163=16×16=25616^3 = 16 \times 16 = 256. (i) What mistake did she make? (ii) Find the correct value of 16316^3 by first finding 16×1616 \times 16. (iii) In the same way, find 11311^3.
    5 marks
    Answer and solution

    (i) She multiplied 16 by itself only 2 times. 16316^3 needs 3 factors of 16.

    (ii) 16×16=25616 \times 16 = 256, 256×16=4096256 \times 16 = 4096

    (iii) 11×11=12111 \times 11 = 121, 121×11=1331121 \times 11 = 1331

    Answer: (ii) 163=409616^3 = 4096 (iii) 113=133111^3 = 1331

  8. Is (−25)3(-25)^3 a positive or a negative number? Explain without finding its value.
    1 mark
    Answer and solution

    (−25)3=−253(-25)^3 = -25^3

    The cube of a negative number is negative.

    Answer: Negative

  9. Find the values of (−7)3(-7)^3 and (−9)3(-9)^3.
    2 marks
    Answer and solution

    (−7)3=−73=−343(-7)^3 = -7^3 = -343

    9×9=819 \times 9 = 81, 81×9=72981 \times 9 = 729

    ∴(−9)3=−729\therefore (-9)^3 = -729

    Answer: (−7)3=−343(-7)^3 = -343, (−9)3=−729(-9)^3 = -729

  10. Find the cubes of −8-8, −10-10 and −12-12.
    3 marks
    Answer and solution

    (−8)3=−83=−(64×8)=−512(-8)^3 = -8^3 = -(64 \times 8) = -512

    (−10)3=−103=−(100×10)=−1000(-10)^3 = -10^3 = -(100 \times 10) = -1000

    (−12)3=−123=−(144×12)=−1728(-12)^3 = -12^3 = -(144 \times 12) = -1728

    Answer: (−8)3=−512(-8)^3 = -512, (−10)3=−1000(-10)^3 = -1000, (−12)3=−1728(-12)^3 = -1728

  11. Find 23+732^3 + 7^3.
    1 mark
    Answer and solution

    23+73=8+3432^3 + 7^3 = 8 + 343

    =351= 351

    Answer: 351351

  12. Find the sum of the cubes of the first 6 natural numbers.
    5 marks
    Answer and solution

    13+23+33+43+53+63=1+8+27+64+125+2161^3 + 2^3 + 3^3 + 4^3 + 5^3 + 6^3 = 1 + 8 + 27 + 64 + 125 + 216

    =441= 441

    Answer: 441441

  13. Find 93+(−9)39^3 + (-9)^3.
    1 mark
    Answer and solution

    (−9)3=−93(-9)^3 = -9^3

    93+(−9)3=93−93=09^3 + (-9)^3 = 9^3 - 9^3 = 0

    Answer: 00

  14. Find the value of 53+(−8)35^3 + (-8)^3.
    2 marks
    Answer and solution

    53+(−8)3=125+(−512)5^3 + (-8)^3 = 125 + (-512)

    =125−512= 125 - 512

    =−387= -387

    Answer: −387-387

  15. How much more is the cube of 10 than the cube of 7?
    2 marks
    Answer and solution

    Difference = 103−7310^3 - 7^3

    103−73=1000−34310^3 - 7^3 = 1000 - 343

    =657= 657

    Answer: 657657

  16. Find the value of 113−13311^3 - 13^3.
    3 marks
    Answer and solution

    113=121×11=133111^3 = 121 \times 11 = 1331

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

    113−133=1331−219711^3 - 13^3 = 1331 - 2197

    =−866= -866

    Answer: −866-866

  17. Kiran wrote: 113−143=(11−14)3=(−3)3=−2711^3 - 14^3 = (11 - 14)^3 = (-3)^3 = -27. (i) Find the correct value of 113−14311^3 - 14^3. (ii) What was Kiran's mistake?
    5 marks
    Answer and solution

    (i) 113=121×11=133111^3 = 121 \times 11 = 1331

    143=196×14=274414^3 = 196 \times 14 = 2744

    113−143=1331−2744=−141311^3 - 14^3 = 1331 - 2744 = -1413

    (ii) Each number must be cubed first and then subtracted. 113−14311^3 - 14^3 is not (11−14)3(11 - 14)^3.

    Answer: (i) −1413-1413 (ii) He subtracted the numbers before cubing them

  18. Simplify t3−(−t)3t^3 - (-t)^3.
    1 mark
    Answer and solution

    (−t)3=−t3(-t)^3 = -t^3

    t3−(−t3)=t3+t3=2t3t^3 - (-t^3) = t^3 + t^3 = 2t^3

    Answer: 2t32t^3

  19. Arrange in ascending order: (−4)3(-4)^3, 333^3, −23-2^3, (−5)3(-5)^3, 131^3.
    3 marks
    Answer and solution

    (−4)3=−64(-4)^3 = -64, 33=273^3 = 27, −23=−8-2^3 = -8, (−5)3=−125(-5)^3 = -125, 13=11^3 = 1

    −125<−64<−8<1<27-125 < -64 < -8 < 1 < 27

    So the order is (−5)3(-5)^3, (−4)3(-4)^3, −23-2^3, 131^3, 333^3.

    Answer: (−5)3(-5)^3, (−4)3(-4)^3, −23-2^3, 131^3, 333^3

  20. Simplify −63+(−2)3−(−5)3+33-6^3 + (-2)^3 - (-5)^3 + 3^3.
    5 marks
    Answer and solution

    −63+(−2)3−(−5)3+33=−216+(−8)−(−125)+27-6^3 + (-2)^3 - (-5)^3 + 3^3 = -216 + (-8) - (-125) + 27

    =−216−8+125+27= -216 - 8 + 125 + 27

    =−72= -72

    Answer: −72-72