An architect designs a building with glass on all sides, solar panels on the roof, and an underground garage. To determine the amount of glass required, the architect creates this scale model. What amount of glass, in square meters (m²), is needed for the building? 50 cm Scale 1:240 40 cm ©2019 StrongMind. O 37,440 m² O 24,660 m² O 18,720 m² O 6500 m² 25 cm
An architect designs a building with glass on all sides, solar panels on the roof, and an underground garage. To determine the amount of glass required, the architect creates this scale model. What amount of glass, in square meters (m²), is needed for the building? 50 cm Scale 1:240 40 cm ©2019 StrongMind. O 37,440 m² O 24,660 m² O 18,720 m² O 6500 m² 25 cm
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:## Calculation of Glass Surface Area for Architectural Building Design
An architect designs a building with glass on all sides, solar panels on the roof, and an underground garage. To determine the amount of glass required, the architect creates this scale model.
**Scale Model Dimensions:**
- Height: 50 cm
- Length: 40 cm
- Width: 25 cm
- Scale: 1:240
The task is to calculate the required amount of glass in square meters (m²) for the actual building using the given scale model.
### Diagram Analysis
The diagram depicts a rectangular prism representing the scale model of the building. The prism's dimensions are labeled:
- Height: 50 cm
- Length: 40 cm
- Width: 25 cm
A note indicates the scale ratio of 1:240.
### Calculation
To find the required amount of glass in square meters:
1. **Calculate the actual dimensions of the building from the scale.**
- Actual height: 50 cm * 240 = 12,000 cm = 120 m
- Actual length: 40 cm * 240 = 9,600 cm = 96 m
- Actual width: 25 cm * 240 = 6,000 cm = 60 m
2. **Calculate the surface area of the sides where glass is applied.**
- Front and Back Surface Area: 2 * (height * width) = 2 * (120 m * 60 m) = 2 * 7,200 m² = 14,400 m²
- Left and Right Surface Area: 2 * (height * length) = 2 * (120 m * 96 m) = 2 * 11,520 m² = 23,040 m²
3. **Total Glass Surface Area = Front and Back Surface Area + Left and Right Surface Area = 14,400 m² + 23,040 m² = 37,440 m².**
### Answer Options
- ☐ 37,440 m²
- ☐ 24,660 m²
- ☐ 18,720 m²
- ☐ 6500 m²
The correct option is **37,440 m²**.
© 2019 StrongMind.
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