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ANNEXURE B represents a South African map. Answer the questions below based on the annexure.

Mathematics

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Here are the solutions to the problems:

4.1
Questions 4.1.1, 4.1.2, 4.1.3, and 4.1.4 require "ANNEXURE B", which is a South African map. This annexure is not provided in the image, so these questions cannot be answered.

4.2
This question requires the distance between Bloemfontein and Messina. This distance would typically be derived from a map (Annexure B, as suggested by question 4.1.3). Since the map is not provided, the distance is unknown, and therefore, the arrival time cannot be calculated.

4.3.1

  1. Identify the given dimensions and formula.

    The height of the tank is h=1200h = 1200 mm.
    The diameter of the tank is d=870d = 870 mm.
    The formula for the volume of a cylinder is V=3.142×radius2×heightV = 3.142 \times \text{radius}^2 \times \text{height}.

  2. Calculate the radius from the diameter.

    The radius (rr) is half of the diameter.

    r=d2=870 mm2=435 mmr = \frac{d}{2} = \frac{870 \text{ mm}}{2} = 435 \text{ mm}

  3. Substitute the values into the volume formula.

    V=3.142×(435 mm)2×1200 mmV = 3.142 \times (435 \text{ mm})^2 \times 1200 \text{ mm} V=3.142×189225 mm2×1200 mmV = 3.142 \times 189225 \text{ mm}^2 \times 1200 \text{ mm}

  4. Calculate the volume.

    V=3.142×227070000 mm3V = 3.142 \times 227070000 \text{ mm}^3 V=713453940 mm3V = 713453940 \text{ mm}^3

    This calculated volume matches the volume given in the problem statement.

    4.3.2

  5. Use the volume calculated in 4.3.1.

    The volume of the tank is V=713453940 mm3V = 713 453 940 \text{ mm}^3.

  6. Use the given conversion factor.

    1 litre = 1 000 000 mm3^3.

  7. Convert the volume from mm3^3 to litres.

    Vlitres=713453940 mm31000000 mm3/litreV_{\text{litres}} = \frac{713 453 940 \text{ mm}^3}{1 000 000 \text{ mm}^3/\text{litre}} Vlitres=713.45394 litresV_{\text{litres}} = 713.45394 \text{ litres}

  8. Round the answer to the nearest litre.

    Vlitres≈713 litresV_{\text{litres}} \approx 713 \text{ litres}

    The volume of the tank in litres, rounded to the nearest litre, is 713 litres\boxed{\text{713 litres}}.

    4.3.3

  9. Identify the diameter of the tank.

    The diameter of the tank is d=870d = 870 mm.

  10. Convert the diameter from millimeters (mm) to centimeters (cm).

    Since 1 cm = 10 mm:

    d=870 mm10 mm/cm=87 cmd = \frac{870 \text{ mm}}{10 \text{ mm/cm}} = 87 \text{ cm}

  11. Convert the diameter from centimeters (cm) to inches.

    Given that 1 inch = 2.54 cm:

    dinches=87 cm2.54 cm/inchd_{\text{inches}} = \frac{87 \text{ cm}}{2.54 \text{ cm/inch}} dinches≈34.2519685 inchesd_{\text{inches}} \approx 34.2519685 \text{ inches}

  12. Round the answer to two decimal places.

    dinches≈34.25 inchesd_{\text{inches}} \approx 34.25 \text{ inches}

    The diameter of the tank in inches, rounded to two decimal places, is 34.25 inches\boxed{\text{34.25 inches}}.

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