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Grade 10 Math Lab: Proof & Generalization FREE
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Surface Area of 3D Solids
Learning Objectives
- Calculate surface area of prisms and cylinders
- Work with nets
- Solve optimization problems
Key Concepts
Surface Area
Total area of all faces of a 3D solid
Net
2D unfolding of a 3D shape
Theory
**Surface Area Formulas:**
- Rectangular prism: SA = 2(lw + lh + wh)
- Cylinder: SA = 2πr² + 2πrh
- Sphere: SA = 4πr²
- Cone: SA = πr² + πrl (l = slant height)
**Optimization:** For a given volume, the shape with minimum surface area is a sphere.
Examples
SA of cylinder r=3, h=5
Solution: SA = 2π(9) + 2π(3)(5) = 18π + 30π = 48π ≈ 150.8