Question
5. The diameter of the moon is 2160 miles. A model has a scale of 1 inch \( =150 \) miles. What is the diameter of the model( inches)?
Ask by Long Guzman. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The model Moon's diameter is 14.4 inches.
Solution
To determine the diameter of the model Moon based on the given scale, follow these steps:
**Given:**
- **Actual diameter of the Moon:** 2,160 miles
- **Scale of the model:** 1 inch \( = \) 150 miles
**Step 1: Understand the Scale**
The scale tells us that **1 inch** on the model represents **150 miles** in reality.
**Step 2: Set Up the Proportion**
To find out how many inches the model's diameter will be, use the following proportion:
\[
\frac{1 \text{ inch}}{150 \text{ miles}} = \frac{x \text{ inches}}{2,160 \text{ miles}}
\]
**Step 3: Solve for \( x \) (the model's diameter in inches)**
\[
x = \frac{2,160 \text{ miles} \times 1 \text{ inch}}{150 \text{ miles}} = \frac{2,160}{150} = 14.4 \text{ inches}
\]
**Answer:**
The diameter of the model Moon is **14.4 inches**.
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To find the diameter of the model, you need to divide the actual diameter of the moon by the scale factor. So, take the diameter of the moon, 2160 miles, and divide it by 150 miles per inch. Calculating it gives you: \[ \text{Model Diameter} = \frac{2160 \text{ miles}}{150 \text{ miles/inch}} = 14.4 \text{ inches} \] So, the diameter of the model is 14.4 inches! If you're ever confused with scaling down sizes, remember the golden rule: maintain the ratio! It’s tempting to shortcut your way, but miscalculating the scale can lead to models that don't represent the actual sizes correctly. Always double-check your arithmetic!
