An artist built a scale model of a skyscraper using a scale in which 3 centimeters represents 45 meters. The height of the skyscraper is 360 meters.

What is the height of the scale model in centimeters?

Use the drop-down to complete the sentence.

The height of the scale model is (Select)   centimeters.

To determine the height of the scale model in centimeters, we can set up a proportion based on the given scale: 3 centimeters represents 45 meters.

Let \( x \) be the height of the scale model in centimeters. The proportion is:

\[
\frac{3}{45} = \frac{x}{360}
\]

Cross-multiply to solve for \( x \):

\[
3 \times 360 = 45 \times x
\]

\[
1080 = 45x
\]

Now, divide both sides by 45:

\[
x = \frac{1080}{45} = 24
\]

Thus, the height of the scale model is **24 centimeters**.

Do you have any questions or want further details? Here are some related questions:

1. How do you determine the scale ratio in other similar problems?
2. If the model height was 30 cm, what would be the skyscraper's actual height?
3. What if the scale was 1 cm = 30 meters? How would the model's height change?
4. How can you convert between different units (e.g., cm to inches) when working with scale models?
5. What other real-world objects could benefit from using a scale model?

**Tip:** Always check that both parts of a scale problem use consistent units before solving.

An artist built a scale model of a skyscraper using a scale in which 3 centimeters represents 45 meters. The height of the skyscraper is 360 meters. What is the height of the scale model in centimeters?

Learn how to find the height of a scale model when an artist uses a scale where 3 cm represents 45 meters. With the skyscraper's actual height being 360 meters, this problem helps in understanding proportions, ratios, and scale models. Suitable for Grades 6-8.

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