Final answer:
The scale factor of a drawing with a scale of '1 inch = 1 foot' is 1/12, as this represents the ratio of the drawing's dimensions to the actual dimensions when both are expressed in the same units. To find other scale factors, feet must be converted to inches and the ratio simplified.
Step-by-step explanation:
The scale factor of a drawing or model is the ratio of any single measurement on the drawing to the corresponding actual measurement of the object. To calculate the scale factor when given a scale in the format of '1 inch = X feet', we convert the given scale to the same units. In the case provided, the scale is '1 inch = 1 foot', which simplifies to '1 inch = 12 inches' (since there are 12 inches in a foot). Hence, the scale factor is 1/12 since every inch on the drawing represents 12 inches in real life.
For example, if we consider a scale of '1 inch = 10 feet', the first step is to write the ratio as '1 inch/10 feet' or '1 inch/120 inches' after converting feet to inches. This simplification would then give us the scale factor of 1/120.
Scale Factor Calculation Examples:
- For a scale of '2 inches/8 feet', the ratio converts to '2 inches/96 inches', giving a scale factor of 1/48.
- To find the scale factor with '3 inches/12 feet', we convert it to '3 inches/144 inches' which simplifies to a scale factor of 1/48.
Understanding and correctly applying scale factors is crucial in creating accurate representations in scale drawings and models and is a key skill in subjects such as engineering, architecture, and graphic design.