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Explain the scale 1:100 and calculate the dimensions of a seat on a drawing if its real-life dimensions are 0.5m x 0.5m. Also, explain the importance of scale drawings.

Mathematics

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Answer

0.5 cm×0.5 cm\text{0.5 cm} \times \text{0.5 cm}

Step-by-step solution

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3.2.1 The scale 1:1001:100 means that 1 unit of length on the drawing represents 100 units of the same length in real life. For example, 1 cm1 \text{ cm} on the drawing corresponds to 100 cm100 \text{ cm} (or 1 m1 \text{ m}) in the actual cinema.

3.2.2

  1. Convert the real-life seat dimension from meters to centimeters.

    0.5 m=0.5×100 cm=50 cm0.5 \text{ m} = 0.5 \times 100 \text{ cm} = 50 \text{ cm}
  2. Apply the scale $1:100$ to find the dimension on the drawing.

    Scaled dimension=50 cm100=0.5 cm\text{Scaled dimension} = \frac{50 \text{ cm}}{100} = 0.5 \text{ cm}

    A scaled diagram of one seat would be a square with sides measuring 0.5 cm×0.5 cm\boxed{\text{0.5 cm} \times \text{0.5 cm}}.

    3.2.3 Working with scale drawings is important because it allows for accurate visualization and planning of space and layout, ensuring that all components fit correctly and that there is adequate room for movement and facilities before construction.

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