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 solve the problem, we can use a proportion based on the given scale.

The scale is \( 2 \text{ inches} \) representing \( 30 \text{ feet} \). We are asked to find the height of the scale model that represents a stadium with a height of \( 180 \text{ feet} \).

The proportion is:

\[
\frac{2 \text{ inches}}{30 \text{ feet}} = \frac{x \text{ inches}}{180 \text{ feet}}
\]

Now solve for \( x \):

\[
\frac{2}{30} = \frac{x}{180}
\]

Cross-multiply:

\[
2 \times 180 = 30 \times x
\]

\[
360 = 30x
\]

Solve for \( x \):

\[
x = \frac{360}{30} = 12 \text{ inches}
\]

So, the height of the scale model is **12 inches**.

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

Would you like further details or have any questions?

Here are 5 related questions to explore:
1. What would be the height of the scale model if the stadium height was 240 feet?
2. If the scale was changed to 1 inch representing 15 feet, what would be the new height of the model for a 180-foot stadium?
3. How many feet does 1 inch represent in this model?
4. What is the total volume of the stadium if it was also scaled down, and the original stadium’s volume was 5,000,000 cubic feet?
5. How does the scale affect the perception of other dimensions like length and width?

**Tip**: Always verify the unit consistency in scale model problems to avoid confusion.

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 solve a scale model problem where 2 inches represents 30 feet and find the height of a scale model for a stadium that's 180 feet tall. This problem focuses on proportions and basic algebra, ideal for Grades 6-8 students.

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