Austria · Klasse 9 · Practice Sheet 38

1. 1.

   A right-angled triangle has legs of 17 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A cylinder has radius 13 cm and height 30 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   Find the gravitational potential energy of a 8 kg object raised 21 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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4. 4.

   €2,700 is invested at 5% compound interest per annum for 5 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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5. 5.

   €2,900 is invested at 8% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

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

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6. 6.

   A circle has a radius of 3 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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7. 7.

   €3,200 is invested at 5% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

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

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8. 8.

   A value changes from 168 to 33. 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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9. 9.

   €4,700 is invested at 3% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

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

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10. 10.

    Find the gravitational potential energy of a 45 kg object raised 31 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    €36 is shared in the ratio 1 : 2. Find each share.

    Formula:Dividing in a Ratio

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

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12. 12.

    An object has mass 105.6 g and volume 22 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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13. 13.

    A force of 220 N acts on an area of 8.4 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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14. 14.

    A train moves at 75 km/h for 4.3 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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15. 15.

    An object has mass 94 g and volume 47 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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16. 16.

    A train moves at 21 km/h for 2.2 hours. How far does it travel?

    Formula:Distance from Speed & Time

    $d = v \times t$

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17. 17.

    Find the force needed to accelerate a 44 kg mass at 4.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    A force of 40 N moves an object 39 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A circle has a radius of 22 cm. Find its area. (Use π ≈ 3.14159)

    Formula:Area of a Circle

    $A = \pi r^2$

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20. 20.

    Find the momentum of a 52 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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