Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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D, E, F
![### Unit Conversion Problems
#### Given Problems:
c. Convert 9 cm² to mm²
d. Convert 3 km² to m²
e. Convert 10⁶ m² to km²
f. Convert 10¹² mm² to m²
#### Partially Solved Example:
a. Convert 10 m² to cm²
Given Solution:
\[ 10 \text{ m}^2 = 100000 \text{ cm}^2 \]
**Note:** Simplify your answer as needed. Type and verify each step to ensure accuracy in your conversions.
#### Explanations:
1. **Conversion from square centimeters to square millimeters (Problem c):**
- \( 1 \text{ cm}^2 = 100 \text{ mm}^2 \)
- Therefore, \( 9 \text{ cm}^2 = 9 \times 100 \text{ mm}^2 = 900 \text{ mm}^2 \)
2. **Conversion from square kilometers to square meters (Problem d):**
- \( 1 \text{ km}^2 = 1,000,000 \text{ m}^2 \)
- Therefore, \( 3 \text{ km}^2 = 3 \times 1,000,000 \text{ m}^2 = 3,000,000 \text{ m}^2 \)
3. **Conversion from square meters to square kilometers (Problem e):**
- \( 10^6 \text{ m}^2 = 1 \text{ km}^2 \)
- Therefore, \( 10^6 \text{ m}^2 = 1 \text{ km}^2 \)
4. **Conversion from square millimeters to square meters (Problem f):**
- \( 1 \text{ mm}^2 = 1 \times 10^{-6} \text{ m}^2 \)
- Therefore, \( 10^{12} \text{ mm}^2 = 10^{12} \times 10^{-6} \text{ m}^2 = 10^6 \text{ m}^2 \)](https://content.bartleby.com/qna-images/question/a6506383-1f6c-4925-93a1-d439ea45d460/9294d4b2-34ec-4116-9842-7c82e7054c01/5wddpc_processed.jpeg)
Transcribed Image Text:### Unit Conversion Problems
#### Given Problems:
c. Convert 9 cm² to mm²
d. Convert 3 km² to m²
e. Convert 10⁶ m² to km²
f. Convert 10¹² mm² to m²
#### Partially Solved Example:
a. Convert 10 m² to cm²
Given Solution:
\[ 10 \text{ m}^2 = 100000 \text{ cm}^2 \]
**Note:** Simplify your answer as needed. Type and verify each step to ensure accuracy in your conversions.
#### Explanations:
1. **Conversion from square centimeters to square millimeters (Problem c):**
- \( 1 \text{ cm}^2 = 100 \text{ mm}^2 \)
- Therefore, \( 9 \text{ cm}^2 = 9 \times 100 \text{ mm}^2 = 900 \text{ mm}^2 \)
2. **Conversion from square kilometers to square meters (Problem d):**
- \( 1 \text{ km}^2 = 1,000,000 \text{ m}^2 \)
- Therefore, \( 3 \text{ km}^2 = 3 \times 1,000,000 \text{ m}^2 = 3,000,000 \text{ m}^2 \)
3. **Conversion from square meters to square kilometers (Problem e):**
- \( 10^6 \text{ m}^2 = 1 \text{ km}^2 \)
- Therefore, \( 10^6 \text{ m}^2 = 1 \text{ km}^2 \)
4. **Conversion from square millimeters to square meters (Problem f):**
- \( 1 \text{ mm}^2 = 1 \times 10^{-6} \text{ m}^2 \)
- Therefore, \( 10^{12} \text{ mm}^2 = 10^{12} \times 10^{-6} \text{ m}^2 = 10^6 \text{ m}^2 \)
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