Question
Jessica created a scale model of the Statue of Liberty that had a height 30 1
2 in. The Statue of
Liberty has an actual height of 305 feet.
Which scale did Jessica use to create the scale model of the Statue of Liberty?
Responses
A
1 inch represents 1
2 foot
1 inch represents 1 2 foot
B 1 inch represents 10 feet1 inch represents 10 feet
C
10 inches represents 1
2 foot
10 inches represents 1 2 foot
D 10 inches represents 1 foot
2 in. The Statue of
Liberty has an actual height of 305 feet.
Which scale did Jessica use to create the scale model of the Statue of Liberty?
Responses
A
1 inch represents 1
2 foot
1 inch represents 1 2 foot
B 1 inch represents 10 feet1 inch represents 10 feet
C
10 inches represents 1
2 foot
10 inches represents 1 2 foot
D 10 inches represents 1 foot
Answers
GPT-4o mini
To find the scale Jessica used, we need to compare the height of her scale model to the actual height of the Statue of Liberty.
1. **Convert the height of the scale model from inches to feet.**
- The scale model height is \(30 \frac{1}{2}\) inches, which can be converted to feet:
\[
30 \frac{1}{2} \text{ inches} = 30.5 \text{ inches}
\]
Since there are 12 inches in a foot, we convert inches to feet:
\[
30.5 \text{ inches} \div 12 = \frac{30.5}{12} = 2.54167 \text{ feet} \approx 2.54 \text{ feet}
\]
2. **Identify the actual height in feet.**
- The actual height of the Statue of Liberty is 305 feet.
3. **Determine the scale.**
- We can find the scale by comparing these two heights:
\[
\text{Scale} = \frac{\text{Actual height}}{\text{Model height}} = \frac{305}{2.54} \approx 120.87
\]
This implies that 1 inch of the model represents approximately 12.5 feet in real life, which can simplify to a scale of approximately 1 inch representing 1 foot.
4. **Evaluate the response options given:**
- **Option A:** 1 inch represents \( \frac{1}{2} \) foot - Not correct.
- **Option B:** 1 inch represents 10 feet - Not correct.
- **Option C:** 10 inches represents \( \frac{1}{2} \) foot - Not correct.
- **Option D:** 10 inches represents 1 foot - This is correct as it corresponds to a scale where 1 inch in the model would correspond to 10 feet in reality.
Therefore, the correct scale that Jessica used to create the scale model of the Statue of Liberty is:
**D: 10 inches represents 1 foot.**
1. **Convert the height of the scale model from inches to feet.**
- The scale model height is \(30 \frac{1}{2}\) inches, which can be converted to feet:
\[
30 \frac{1}{2} \text{ inches} = 30.5 \text{ inches}
\]
Since there are 12 inches in a foot, we convert inches to feet:
\[
30.5 \text{ inches} \div 12 = \frac{30.5}{12} = 2.54167 \text{ feet} \approx 2.54 \text{ feet}
\]
2. **Identify the actual height in feet.**
- The actual height of the Statue of Liberty is 305 feet.
3. **Determine the scale.**
- We can find the scale by comparing these two heights:
\[
\text{Scale} = \frac{\text{Actual height}}{\text{Model height}} = \frac{305}{2.54} \approx 120.87
\]
This implies that 1 inch of the model represents approximately 12.5 feet in real life, which can simplify to a scale of approximately 1 inch representing 1 foot.
4. **Evaluate the response options given:**
- **Option A:** 1 inch represents \( \frac{1}{2} \) foot - Not correct.
- **Option B:** 1 inch represents 10 feet - Not correct.
- **Option C:** 10 inches represents \( \frac{1}{2} \) foot - Not correct.
- **Option D:** 10 inches represents 1 foot - This is correct as it corresponds to a scale where 1 inch in the model would correspond to 10 feet in reality.
Therefore, the correct scale that Jessica used to create the scale model of the Statue of Liberty is:
**D: 10 inches represents 1 foot.**