Austria · Klasse 9 · Practice Sheet 15

1. 1.

   A cone has base radius 10 cm and height 10 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.

   A car travels 375 km in 5 hours. Find its average speed.

   Formula:Speed

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

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3. 3.

   Solve for x: 3x + 13 = 43.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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4. 4.

   A bag has 9 equally likely marbles, of which 4 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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5. 5.

   Find the circumference of a circle whose radius is 28 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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6. 6.

   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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7. 7.

   A force of 41 N acts on an area of 3.9 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A train moves at 55 km/h for 2.2 hours. How far does it travel?

   Formula:Distance from Speed & Time

   $d = v \times t$

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9. 9.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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10. 10.

    A bag has 24 equally likely marbles, of which 11 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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11. 11.

    Find the circumference of a circle whose radius is 19 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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12. 12.

    A cylinder has radius 10 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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13. 13.

    Find the momentum of a 41 kg object moving at 3 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A device runs at 55 V drawing 4.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the force needed to accelerate a 16 kg mass at 5.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A force of 390 N acts on an area of 3.9 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A 21 kg object moves at 20 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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18. 18.

    A value changes from 44 to 125. 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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19. 19.

    A cone has base radius 4 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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20. 20.

    A force of 328 N acts on an area of 6.4 m². Find the pressure.

    Formula:Pressure

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

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