An architect built a scale model of a sports stadium using a scale in which 2 inches represents 30 feet. The height of the sports stadium is 180 feet.

What is the height of the scale model in inches?

A.3 in.

B.12 in.

C.60 in.

D.105 in.

To determine the height of the scale model, we can use a proportion based on the given scale. The problem states that 2 inches on the model represents 30 feet of the actual stadium height.

### Set up the proportion:
\[
\frac{\text{Model Height (inches)}}{\text{Actual Height (feet)}} = \frac{2 \, \text{inches}}{30 \, \text{feet}}
\]

The actual height of the stadium is 180 feet, so let the model height be \( x \) inches. The proportion becomes:
\[
\frac{x}{180} = \frac{2}{30}
\]

### Solve for \( x \):
\[
x = \frac{2}{30} \times 180
\]

First, simplify:
\[
\frac{2}{30} = \frac{1}{15}
\]

Now calculate:
\[
x = \frac{1}{15} \times 180 = 12 \, \text{inches}
\]

### Answer:
The height of the scale model is **12 inches**.

The correct answer is **B. 12 in.**

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Do you want more details or have any questions?

Here are 5 related questions to expand on this:
1. If the actual height was 240 feet, what would the model height be?
2. How would the model height change if the scale was 1 inch representing 15 feet?
3. What is the total scale factor between the model and the actual stadium?
4. How long would a 90-foot structure be on the model?
5. How many inches on the model would represent 360 feet of the actual stadium?

**Tip:** Always check the units when setting up a proportion to avoid errors.

An architect built a scale model of a sports stadium using a scale in which 2 inches represents 30 feet. The height of the sports stadium is 180 feet. What is the height of the scale model in inches?
A. 3 in.
B. 12 in.
C. 60 in.
D. 105 in.

Learn how to calculate the height of a scale model of a sports stadium using a ratio of 2 inches to 30 feet. In this problem, the actual stadium height is 180 feet. Find out how to set up proportions and solve for the model height, with a detailed step-by-step solution. Suitable for Grades 6-8 students.

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