The scale model of a skyscraper being built is 4.2 feet tall.
a. When it is finished, the skyscraper will be 525 meters tall. What scale was used to make the model?
The correct answer and explanation is :
To find the scale used to make the model of the skyscraper, we need to compare the height of the model to the actual height of the skyscraper in the same units.
Given:
- The height of the model is 4.2 feet.
- The height of the finished skyscraper is 525 meters.
Step 1: Convert the height of the skyscraper from meters to feet.
We know that 1 meter is approximately equal to 3.28084 feet. To convert 525 meters into feet, we multiply by this conversion factor:
$$
525 \, \text{meters} \times 3.28084 \, \frac{\text{feet}}{\text{meter}} = 1,719.94 \, \text{feet}
$$
So, the height of the skyscraper in feet is approximately 1,719.94 feet.
Step 2: Determine the scale.
The scale of the model is the ratio of the height of the model to the height of the actual skyscraper. We can express this ratio as:
$$
\text{Scale} = \frac{\text{Height of the model}}{\text{Height of the actual skyscraper}} = \frac{4.2 \, \text{feet}}{1,719.94 \, \text{feet}}
$$
Now, calculating this:
$$
\frac{4.2}{1,719.94} \approx 0.00244
$$
This means that the scale of the model is 1:410, which is the ratio of the model’s height to the skyscraper’s height.
Conclusion:
The scale used to create the model of the skyscraper is 1:410. This means that every 1 unit of height in the model represents 410 units of height in the actual skyscraper. This scaling allows the model to be a manageable size while maintaining a proportionate representation of the actual skyscraper’s dimensions.
This process involves converting the height units to match, finding the ratio of the model’s height to the real structure’s height, and then expressing it as a scale. This scale can be used in design, construction, and architectural visualization to accurately represent the final building in a compact form.