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Explain bar scales and number scales, and calculate the actual dimensions of objects given their plan dimensions and a scale of 1:50.

Mathematics

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QUESTION 3.1

3.1.1

  • A bar scale is a visual representation of the scale, typically a line marked with distances, which remains accurate even if the map or plan is enlarged or reduced.
  • A number scale (or ratio scale) is expressed as a ratio (e.g., 1:50) or a fraction, indicating that one unit on the plan represents a certain number of the same units in reality. It becomes inaccurate if the map or plan is resized.

3.1.2

The scale 1:50 means that 1 unit of measurement on the plan represents 50 of the same units in actual size. For example, 1 cm on the plan corresponds to an actual length of 50 cm.

3.1.3

  1. Determine the actual length using the scale.

    Plan length of teacher's desk = 6 cm
    Scale = 1:50
    Actual length = Plan length ×\times Scale factor

    Actual length=6 cm×50=300 cm\text{Actual length} = 6 \text{ cm} \times 50 = 300 \text{ cm}

  2. Convert the actual length from centimeters to meters.

    Since 1 meter = 100 centimeters:

    Actual length in meters=300 cm100 cm/m=3 m\text{Actual length in meters} = \frac{300 \text{ cm}}{100 \text{ cm/m}} = 3 \text{ m}

    The actual length of the desk is 3 m\boxed{\text{3 m}}.

    3.1.4

  3. Determine the actual distance using the scale.

    Distance between learners' desks on the plan = 4 cm
    Scale = 1:50
    Actual distance = Plan distance ×\times Scale factor

    Actual distance=4 cm×50=200 cm\text{Actual distance} = 4 \text{ cm} \times 50 = 200 \text{ cm}

  4. Convert the actual distance from centimeters to meters.

    Since 1 meter = 100 centimeters:

    Actual distance in meters=200 cm100 cm/m=2 m\text{Actual distance in meters} = \frac{200 \text{ cm}}{100 \text{ cm/m}} = 2 \text{ m}

    The actual distance between the desks is 2 m\boxed{\text{2 m}}.

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