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A plan uses a scale of 1:200. What are the actual dimensions and floor area of a classroom and a computer lab shown on this plan?

Mathematics

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Answer

2.3 a) Actual Length=7 m\text{2.3 a) Actual Length} = 7 \text{ m}

2.3 a) Actual Width=5 m\text{2.3 a) Actual Width} = 5 \text{ m}

2.3 b) Actual floor area=48 m2\text{2.3 b) Actual floor area} = 48 \text{ m}^2

Step-by-step solution

4 steps
  1. State the assumed scale for the plan.

    For questions 2.3 (a) and (b), it is assumed that the plan uses Scale D, which is a ratio scale of 1:2001 : 200. This means 1 cm1 \text{ cm} on the plan represents 200 cm200 \text{ cm} in actual distance.

  2. Calculate the actual dimensions of the Classroom for 2.3 (a).

    Given:
    Classroom Length on Plan = 3,5 cm3,5 \text{ cm}
    Classroom Width on Plan = 2,5 cm2,5 \text{ cm}
    Scale Denominator = 200

    Actual Length = Plan Length ×\times Scale Denominator

    Actual Length=3,5 cm×200=700 cm\text{Actual Length} = 3,5 \text{ cm} \times 200 = 700 \text{ cm}

    Convert to meters (1 m=100 cm1 \text{ m} = 100 \text{ cm}):

    Actual Length=700 cm100=7 m\text{Actual Length} = \frac{700 \text{ cm}}{100} = 7 \text{ m}

    Actual Width = Plan Width ×\times Scale Denominator

    Actual Width=2,5 cm×200=500 cm\text{Actual Width} = 2,5 \text{ cm} \times 200 = 500 \text{ cm}

    Convert to meters:

    Actual Width=500 cm100=5 m\text{Actual Width} = \frac{500 \text{ cm}}{100} = 5 \text{ m} 2.3 a) Actual Length=7 m\boxed{\text{2.3 a) Actual Length} = 7 \text{ m}} 2.3 a) Actual Width=5 m\boxed{\text{2.3 a) Actual Width} = 5 \text{ m}}
  3. Calculate the actual floor area of the Computer Lab for 2.3 (b).

    Given:
    Computer Lab Length on Plan = 4,0 cm4,0 \text{ cm}
    Computer Lab Width on Plan = 3,0 cm3,0 \text{ cm}
    Scale Denominator = 200

    First, calculate the actual length and width in meters:
    Actual Length = Plan Length ×\times Scale Denominator

    Actual Length=4,0 cm×200=800 cm\text{Actual Length} = 4,0 \text{ cm} \times 200 = 800 \text{ cm}

    Convert to meters:

    Actual Length=800 cm100=8 m\text{Actual Length} = \frac{800 \text{ cm}}{100} = 8 \text{ m}

    Actual Width = Plan Width ×\times Scale Denominator

    Actual Width=3,0 cm×200=600 cm\text{Actual Width} = 3,0 \text{ cm} \times 200 = 600 \text{ cm}

    Convert to meters:

    Actual Width=600 cm100=6 m\text{Actual Width} = \frac{600 \text{ cm}}{100} = 6 \text{ m}

    Now, calculate the actual floor area:
    Actual Floor Area = Actual Length ×\times Actual Width

    Actual Floor Area=8 m×6 m=48 m2\text{Actual Floor Area} = 8 \text{ m} \times 6 \text{ m} = 48 \text{ m}^2 2.3 b) Actual floor area=48 m2\boxed{\text{2.3 b) Actual floor area} = 48 \text{ m}^2}
  4. Address Question 3.

    The image provided only shows the title "QUESTION 3 CALCULATING MAP DISTANCE & DETERMINING THE SCALE" and a key formula. There are no specific sub-questions or tasks to solve under Question 3 in this image.

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