Germany · Klasse 9 · Practice Sheet 18

1. 1.

   A cone has base radius 10 cm and height 22 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.

   €2,700 is invested at 3% 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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3. 3.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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4. 4.

   Find the circumference of a circle whose radius is 22 m. (Use π ≈ 3.14159)

   Formula:Circumference of a Circle

   $C = 2\pi r$

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5. 5.

   A bag has 10 equally likely marbles, of which 5 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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6. 6.

   A device runs at 20 V drawing 6.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   A force of 117 N moves an object 13 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A cylinder has radius 13 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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9. 9.

   Solve for x: 5x + 10 = 60.

   Formula:Solving a Linear Equation

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

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10. 10.

    A value changes from 192 to 164. 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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11. 11.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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12. 12.

    Find the circumference of a circle whose radius is 21 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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13. 13.

    €111 is shared in the ratio 2 : 1. Find each share.

    Formula:Dividing in a Ratio

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

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14. 14.

    A device runs at 140 V drawing 1.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    An object has mass 21.7 g and volume 7 cm³. Find its density.

    Formula:Density

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

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16. 16.

    Solve for x: 7x + 10 = 45.

    Formula:Solving a Linear Equation

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

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17. 17.

    Find the gravitational potential energy of a 45 kg object raised 38 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    A device runs at 52 V drawing 1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A cylinder has radius 6 cm and height 28 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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20. 20.

    Find the circumference of a circle whose radius is 5 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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