Cubes & Cube Roots

17 Grade 9 Mathematics questions on Cubes & Cube Roots, with worked marking schemes. 17 questions are available on this topic in full.

1. Question 1

   1 mark

   A cube-shaped box has volume 512 cm³. What is the length of one side?

   A. 16 cm

   B. 8 cm

   C. 4 cm

   D. 64 cm

   (1 mark)

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2. Question 2

   1 mark

   What is $\sqrt[3]{216}$?

   A. 9

   B. 6

   C. 8

   D. 7

   (1 mark)

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3. Question 3

   2 marks

   Express 1,000 as a power of 10. Then find its cube root.

   (2 marks)

   Marking scheme

   $1,000=10\times 10\times 10$, which is $10^3$. (1)

   The cube root undoes the cube, so $\sqrt[3]{1,000}=\sqrt[3]{10^3}=10$. (1)

   Final answer: $1,000=10^3$ and $\sqrt[3]{1,000}=10$.

4. Question 4

   2 marks

   Work out: 2³ × 3² = ___

   (2 marks)

   Marking scheme

   A power tells you how many times to multiply the base by itself: $2^3=2\times 2\times 2=8$ and $3^2=3\times 3=9$. (1)

   Now multiply the two results: $8\times 9=72$. (1)

   Final answer: $72$.

5. Question 5

   1 mark

   What is the cube of 4?

   A. 12

   B. 48

   C. 16

   D. 64

   (1 mark)

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6. Question 6

   2 marks

   A cubical storage box has a volume of $15625$ cm${}^3$. Find the length of one edge of the box.

   (2 marks)

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7. Question 7

   1 mark

   Evaluate $\sqrt[3]{4913}$.

   A. $17$

   B. $23$

   C. $19$

   D. $13$

   (1 mark)

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8. Question 8

   4 marks

   A cube has a volume of 343 cm³. Find the length of each side and the total surface area.

   (4 marks)

   Marking scheme

   A cube has all edges equal, so its volume is $s^3$ where $s$ is the edge. (1)

   Here $s^3=343$, so $s=\sqrt[3]{343}=7$, because $7\times 7\times 7=343$. (1)

   A cube has $6$ identical square faces, each of area $s^2=7^2=49$ cm${}^2$. (1)

   Total surface area $=6\times 49=294$. (1)

   Final answer: each side is $7$ cm and the surface area is $294$ cm${}^2$.

9. Question 9

   1 mark

   Which number is a perfect cube?

   A. 81

   B. 64

   C. 36

   D. 25

   (1 mark)

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10. Question 10

    1 mark

    Evaluate: $\sqrt[3]{125}$

    A. 25

    B. 5

    C. 10

    D. 15

    (1 mark)

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11. Question 11

    2 marks

    Evaluate: $\sqrt[3]{512}$ − $\sqrt[3]{64}$

    (2 marks)

    Marking scheme

    A cube root asks which number multiplied by itself three times gives the number. $8^3=512$, so $\sqrt[3]{512}=8$; and $4^3=64$, so $\sqrt[3]{64}=4$. (1)

    Subtract: $8-4=4$. (1)

    Final answer: $4$.

12. Question 12

    1 mark

    $\sqrt[3]{8}$ + $\sqrt[3]{27}$ = ___

    A. 5

    B. 6

    C. 7

    D. 3

    (1 mark)

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13. Question 13

    1 mark

    Evaluate: $\sqrt[3]{1000}$

    A. 100

    B. 50

    C. 10

    D. 5

    (1 mark)

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14. Question 14

    1 mark

    2³ + 3³ = ___

    A. 30

    B. 35

    C. 25

    D. 32

    (1 mark)

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15. Question 15

    1 mark

    5³ = ___

    A. 25

    B. 15

    C. 125

    D. 50

    (1 mark)

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16. Question 16

    2 marks

    Find x if x³ = 729.

    (2 marks)

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17. Question 17

    1 mark

    3³ = ___

    A. 18

    B. 30

    C. 9

    D. 27

    (1 mark)

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