A model of a building is built with a scale of 1:22. If the model is 17.8 feet tall, how tall is the actual building? Round your answer to the nearest hundredth, if necessary.

To solve this problem, we need to find the actual height of the building using the scale provided.

The scale given is 1:22, meaning the actual building is 22 times taller than the model. The height of the model is 17.8 feet.

We use the following proportion:

\[
\text{Actual Height} = \text{Model Height} \times \text{Scale Factor}
\]

Substitute the given values:

\[
\text{Actual Height} = 17.8 \times 22
\]

Now, calculate the actual height:

\[
\text{Actual Height} = 391.6 \text{ feet}
\]

Thus, the actual height of the building is **391.6 feet**.

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:
1. What would the model height be if the actual building was 500 feet tall at the same scale?
2. How does changing the scale factor affect the size of the model?
3. If a different model had a scale of 1:50, how tall would it be if the actual building is 600 feet?
4. Can you calculate the volume ratio between the model and the real building using the same scale factor?
5. How would the model’s width change if the scale factor became 1:10 instead of 1:22?

**Tip:** When working with scales, remember that the scale factor applies equally to all dimensions (height, width, etc.).

Solve the problem of determining the actual height of a building from a scale model. With a scale of 1:22 and a model height of 17.8 feet, this solution explains how to calculate the actual building height, resulting in 391.6 feet. Perfect for students in Grades 6-8, learn how to use ratios and proportions in practical scenarios.

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