Taiwan · Grade 9 · Practice Sheet 28

1. 1.

   Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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2. 2.

   A cone has base radius 9 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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3. 3.

   Find the gravitational potential energy of a 39 kg object raised 7 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   A wave has frequency 507 Hz and wavelength 1.1 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A force of 55 N moves an object 11 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A cone has base radius 5 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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7. 7.

   A right-angled triangle has legs of 13 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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8. 8.

   A current of 2.7 A flows through a 35 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   Find the gravitational potential energy of a 28 kg object raised 7 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    A wave has frequency 98 Hz and wavelength 0.55 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A value changes from 159 to 40. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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12. 12.

    A wave has frequency 856 Hz and wavelength 4.67 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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13. 13.

    Find the circumference of a circle whose radius is 24 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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14. 14.

    A car travels 93 km in 3 hours. Find its average speed.

    Formula:Speed

    $v = \dfrac{d}{t}$

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15. 15.

    NT$ 120 is shared in the ratio 2 : 3. Find each share.

    Formula:Dividing in a Ratio

    $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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16. 16.

    Find the momentum of a 37 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    Find the circumference of a circle whose radius is 11 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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18. 18.

    Find the force needed to accelerate a 41 kg mass at 6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    A right-angled triangle has legs of 16 cm and 10 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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20. 20.

    NT$ 3,500 is invested at 8% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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