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A map has a scale of 1:80,000. Question 1.1: Which statement best describes the scale? A) 1 unit on the map represents 80,000 units in reality. B) 1cm on the map represents 80,000cm in reality. C) Bot

Mathematics

ScanSolve AI Answer

Answer

C

Step-by-step solution

4 steps
  1. Analyze Question 1.1.

    A number scale of 1:80 0001:80\,000 means that one unit of distance on the map represents 80 00080\,000 of the same units of distance in reality.

    • Option A states "1 unit on the map, represents 80 000 units in reality." This is a correct general interpretation.
    • Option B states "1cm on the map, represents 80 000 cm in reality." This is a correct specific interpretation. Since both A and B are correct, the most comprehensive answer is C.

    The correct option is C.

  2. Analyze Question 1.2.

    The map scale is 1:80 0001:80\,000.
    The distance on the map is 18 cm.
    This means 1 cm on the map represents 80 00080\,000 cm in reality.
    To find the actual distance in cm:

    Actual distance=18 cm×80 000\text{Actual distance} = 18 \text{ cm} \times 80\,000 Actual distance=1 440 000 cm\text{Actual distance} = 1\,440\,000 \text{ cm}

    Now, convert centimeters to kilometers.
    We know that 1 m =100= 100 cm and 1 km =1 000= 1\,000 m.
    So, 1 km =1 000×100= 1\,000 \times 100 cm =100 000= 100\,000 cm.
    To convert 1 440 0001\,440\,000 cm to km:

    Actual distance in km=1 440 000 cm100 000 cm/km\text{Actual distance in km} = \frac{1\,440\,000 \text{ cm}}{100\,000 \text{ cm/km}} Actual distance in km=14.4 km\text{Actual distance in km} = 14.4 \text{ km}

    The correct option is A.

  3. Analyze Question 1.3.

    Examine the bar scale provided. The bar scale shows segments representing $0$m, $1$m, $2$m, and $4$m. Below the bar, there is a ruler marking in centimeters. The segment from $0$m to $1$m on the bar corresponds to 1 cm on the ruler marking.
    This means that 1 cm on the map represents 1 m in reality.

    • Option A states "1cm on the map, represents 1m in reality." This matches our observation.
    • Option B states "5cm on the map, represents 4m in reality." If $1$cm represents $1$m, then $5$cm would represent $5$m. So, B is incorrect.
    • Option C states "1m on the map, represents 1cm in reality." This is the inverse and incorrect.

    The correct option is A.

  4. Analyze Question 1.4.

    Locate Port Elizabeth (bottom left) and Mbombela (top right) on the map.
    Trace the major national roads originating from Port Elizabeth.
    The N2 runs along the coast, heading east.
    The N10 heads north-east, inland from Port Elizabeth.
    To travel from Port Elizabeth to Mbombela, the N10 is the first national road that leads in the general direction of Mbombela. The N4 is a road further north, connecting to Mbombela, but it is not the first road from Port Elizabeth.

    The correct option is B.

    Final Answers:
    1.1. The correct option is C.
    1.2. The correct option is A.
    1.3. The correct option is A.
    1.4. The correct option is B.

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