Final answer:
The scale factor Walter used in the drawing is 1:333.33, which is calculated by converting the given scale of 3 millimeters per 1 meter into a ratio and simplifying it. To find actual sizes or apply scale factors, multiply the drawing's measurements by the scale factor (or its reciprocal, if necessary).
Step-by-step explanation:
The scale factor used in scale drawings is a representation of the ratio between the drawing's size and the actual size of the object. For instance, in Walter's drawing of an Italian restaurant with a scale of 3 millimeters to 1 meter, the drawing uses a scale factor of 1:333.33, which is simplified from the ratio 1 millimeter:0.333 meters (since there are 1000 millimeters in a meter). If a student had provided the scale factor of 1/200, which wasn't the case in Walter's scenario, we would know that the actual size is 200 times the size of the drawing. Understanding this concept allows us to solve various problems related to scale models and drawings.
Here are examples illustrating how to use the scale factor:
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- To find the actual dimensions of an object based on the model, multiply the scale dimensions by the scale factor (e.g., 1/200).
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- To calculate the area in actual size, square the scale factor and multiply by the area of the scale model.
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- Given the actual length of an object, divide by the scale factor to find the model's length.
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- For a drawing with a given scale factor, multiply the actual length of the object by the scale factor to find the length in the drawing.
To solve the specific questions provided:
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- The actual floor dimensions would be calculated by multiplying the drawing's dimensions by the scale factor (1/200).
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- The area of the actual floor would be the drawing's area times the square of the scale factor, which is 40,000.
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- The model boat should measure 8 inches long when using a 1/36 scale factor and 4 inches using a 1/72 scale factor.
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- The scale drawing of the metal pipe would measure 2.5 centimeters in length using a 1/100 scale factor.
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- Sydra's drawing would represent the housefly as 80 millimeters or 8 centimeters long using a scale factor of 10.
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- On Calvin's map, the distance between the two houses should be represented as 0.1 centimeters.
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- The actual measurement of a model if the scale is 1 cm = 0.5 m and the scale measurement is 3.2 meters is 1.6 meters.