Find the surface area of the composite figure. Use 3.14 for T.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:**Problem: Find the Surface Area of a Composite Figure**
You are given a composite figure consisting of a cube and a cylinder. Follow these instructions to calculate the surface area.
**Instructions:**
1. **Use 3.14 for π.**
2. **Dimensions:**
- **Cube:**
- Each side measures 9 cm.
- **Cylinder:**
- Height: 4 cm
- Diameter: 6 cm (radius is half of the diameter, so 3 cm)
3. **Calculation for Surface Area:**
- **Cube Surface Area:**
- Formula: \( \text{Surface Area} = 6 \times \text{side}^2 \)
- Calculation: \( 6 \times 9^2 = 486 \, \text{cm}^2 \)
- **Cylinder Surface Area (excluding the base attached to the cube):**
- Formula for the lateral surface area: \( 2 \times \pi \times \text{radius} \times \text{height} \)
- Calculation: \( 2 \times 3.14 \times 3 \times 4 = 75.36 \, \text{cm}^2 \)
- Formula for one circle surface area: \( \pi \times \text{radius}^2 \)
- Calculation: \( 3.14 \times 3^2 = 28.26 \, \text{cm}^2 \)
4. **Combine the Surface Areas (excluding the hidden face of the cylinder):**
- Total Surface Area = Cube Surface Area + Cylinder lateral Surface Area + One Circle Area
- Calculation: \( 486 + 75.36 + 28.26 = 589.62 \, \text{cm}^2 \)
**Conclusion:** The total surface area of the composite figure is approximately \( 589.62 \, \text{cm}^2 \).
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