Germany · Klasse 9 · Practice Sheet 23

1. 1.

   A cone has base radius 9 cm and height 11 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   Find the momentum of a 49 kg object moving at 12 m/s.

   Formula:Momentum

   $p = mv$

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3. 3.

   A right-angled triangle has legs of 11 cm and 18 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   A cylinder has radius 2 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   Find the force needed to accelerate a 35 kg mass at 8.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A car travels 279 km in 3 hours. Find its average speed.

   Formula:Speed

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

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7. 7.

   Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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8. 8.

   A wave has frequency 756 Hz and wavelength 0.76 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   A force of 118 N moves an object 35 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    A train moves at 70 km/h for 2.2 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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11. 11.

    A right-angled triangle has legs of 20 cm and 3 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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12. 12.

    A force of 18 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A train moves at 98 km/h for 3.8 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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14. 14.

    €800 is invested at 10% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

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

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15. 15.

    €3,800 is invested at 4% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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16. 16.

    Find the force needed to accelerate a 35 kg mass at 8.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Find the gravitational potential energy of a 8 kg object raised 5 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A current of 1.2 A flows through a 17 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    Find the gravitational potential energy of a 30 kg object raised 6 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A circle has a radius of 13 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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