Math Problem Statement

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.

Solution

To solve this, we can set up a proportion based on the given scale:

  • The scale is 2 inches for every 30 feet.
  • The actual height of the stadium is 180 feet, and we need to find the height of the scale model in inches.

We can set up the proportion as follows:

2 inches30 feet=x inches180 feet\frac{2 \text{ inches}}{30 \text{ feet}} = \frac{x \text{ inches}}{180 \text{ feet}}

Now, solve for xx:

x=2×18030=36030=12 inchesx = \frac{2 \times 180}{30} = \frac{360}{30} = 12 \text{ inches}

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

The correct answer is B. 12 in.

Do you want further details or have any questions?

Here are 5 related questions:

  1. How would the scale change if 3 inches represented 40 feet?
  2. If the width of the stadium is 300 feet, what would be the width in the model?
  3. How would you calculate the total volume of the stadium and its scale model?
  4. How could you convert this scale into meters?
  5. What would happen to the model's height if the scale changed to 1 inch for 20 feet?

Tip: Setting up proportions is a powerful way to solve problems involving scale models or maps!

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Math Problem Analysis

Mathematical Concepts

Proportions
Ratios
Scale Models

Formulas

Proportion formula: (scale inches/real feet) = (model inches/real feet)

Theorems

Basic Proportion Theorem

Suitable Grade Level

Grades 6-8