Final answer:
The scale factor is a ratio comparing a drawing or model's scale dimensions to the actual object's dimensions. It's used to solve problems involving scale models or drawings by converting dimensions methodically based on the ratio.
Step-by-step explanation:
Understanding Scale Factor
When working with scale drawings or models, the scale factor is an essential concept. It's the ratio that describes how much a drawing or model has been shrunk or enlarged in comparison to the actual object. To find the scale factor, you compare dimensions of the model or drawing (scale dimensions) to the dimensions of the actual object (actual dimensions).
Review of Scale Factor Examples
For a scale of 2 inches to 8 feet, the scale factor would be 1:48 because 2 inches is to 96 inches (8 feet) as 1 is to 48.
A scale of 13 inches to 12 feet is effectively 1:11.08 after converting 12 feet to 144 inches and simplifying.
Using the same method, a scale of 6 inches to 24 feet finds a scale factor of 1:48.
An 11-inch to 33-feet scale yields a scale factor of 1:36.
A scale of 16 inches to 32 feet is 1:24.
Similarly, 18 inches to 36 feet gives a scale factor of 1:24.
A 6-inch to 48-feet scale translates to a scale factor of 1:96.
Finally, a scale of 6 inches to 12 feet is 1:24.
Solving Problems Involving Scale Factor
For problem 9, the scale factor to reduce a 9-inch width to a 2-inch width is 2/9. Problem 10's scale factor for a 4-inch drawing of a 64-inch tall man is 1/16. In problem 11, the map's scale factor of 1 inch to 4 feet is 1:48. For the last scenario, multiplying the dimensions of the box drawing by 3.25 yields the actual dimensions, which would be 6.5 inches by 9.75 inches by 16.25 inches.