An architect is designing a scale model of a building. The actual building is 120 meters tall and the model is 30 centimeters tall. If a window on the actual building is 4 meters wide, what will be the width of the corresponding window on the scale model, in centimeters?
- A2 cm
- B3 cm
- C1.5 cm
- D1 cm
Show answer & explanationAnswer & explanation
Correct answer: D. 1 cm
First, establish the scale factor. The ratio of model height to actual height is 30 cm / 120 m. Convert meters to centimeters: 120 m = 120 * 100 cm = 12000 cm. So, the scale factor is 30 cm / 12000 cm = 1/400. Now, apply this scale factor to the actual window width: 4 meters * (1/400) = 400 cm * (1/400) = 1 cm. Alternatively, set up a proportion: (Model Height / Actual Height) = (Model Window Width / Actual Window Width). (30 cm / 120 m) = (x cm / 4 m). Convert to consistent units: (30 cm / 12000 cm) = (x cm / 400 cm). 30/12000 = x/400. x = (30 * 400) / 12000 = 12000 / 12000 = 1 cm.
Why the other options are wrong
- A. This would be the result of an incorrect scale factor calculation, perhaps 1/200.
- B. This would be the result of an incorrect scale factor or calculation error.
- C. This would be the result of an incorrect scale factor or calculation error.
Scale Factor in Measurement
A scale factor is the ratio by which all dimensions of an object are multiplied to create a scaled version (either larger or smaller) while maintaining proportionality.
- Scale factor = Model dimension / Actual dimension
- All corresponding lengths are scaled by the same factor.
- Units must be consistent when calculating the scale factor (e.g., all cm or all m).
Memory trick: Units match, ratio found, then apply to the new ground!