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Find the surface area of the composite figure. Use 3.14 for T.

Find the surface area of the composite figure. Use 3.14 for T.

Advanced Engineering Mathematics
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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**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 \( 589.62 \, \text{cm}^2 \).
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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