how do i find a scale factor for scale drawings and scale models
What is the scale factor for 1 inch = 20 feet?
When two figures are similar, the reduced ratio of any two corresponding sides is called the scale factor of the similar figure.
Example
One side of a square is 6 and the corresponding side of a similar square is 3.
The ratio is 6 : 3 or 6/3 = 2.
The scale factor is 2 : 1.
To find the scale factor for scale drawings and scale models, you need to compare two corresponding measurements: one on the original object and the other on the scaled representation. Here's a step-by-step guide to help you calculate the scale factor:
1. Identify the corresponding measurements: Select two corresponding measurements on the original object and the scaled representation. For example, you might choose the length of a side on the original object and its corresponding length on the scaled drawing.
2. Measure the original object: Use a ruler or measuring tape to determine the measurement of the selected feature on the original object. Make sure to use the same units for all measurements (e.g., centimeters or inches).
3. Measure the scaled representation: Measure the corresponding feature on the scaled drawing or model using the same units as before. Ensure you measure the length of the corresponding part accurately.
4. Calculate the scale factor: The scale factor is calculated by dividing the measurement of the scaled representation by the measurement of the original object. For example, if the original object's side length is 10 centimeters and the scaled drawing's side length is 2 centimeters, the scale factor would be 2/10, which simplifies to 1/5 or 0.2.
5. Express the scale factor: The scale factor can be expressed in different ways, such as a ratio, fraction, or decimal. It represents how much smaller or larger the scaled representation is compared to the original object.
Remember, scale factors are usually applied uniformly to all dimensions. This means that if you have the scale factor, you can use it to find other corresponding measurements by multiplying or dividing.