Surface Area of Spheres
A sphere's surface area is exactly four times the area of its great circle: .
Introduction
Past Knowledge
Circle area (11.2.3). Great circles. Circumference.
Today's Goal
Apply SA = 4πr² and solve for r given SA.
Future Success
Volume of spheres (12.3.3), similar solids (12.3.4).
Key Concepts
Sphere Surface Area
Exactly 4 great circles. (A great circle is the largest circle on the sphere.)
Hemisphere (Half Sphere)
Half the curved surface (2πr²) + the flat circular base (πr²).
Worked Examples
Sphere SA
r = 7
SA = 196π ≈ 615.8
Find r from SA
SA = 100π. Find r.
→ →
r = 5
Hemisphere
Hemisphere r = 6. Find total SA.
Curved: . Base:
Total:
SA = 108π ≈ 339.3
Common Pitfalls
Hemisphere: Don't Forget the Base
A hemisphere has curved surface 2πr² AND a flat base πr² = total 3πr², not just 2πr².
Real-Life Applications
Painting a Dome
The Capitol dome's interior surface = hemisphere area 2πr². Paint coverage is measured per square foot.
Basketball Material
A basketball (r ≈ 4.7 in): SA = 4π(4.7)² ≈ 278 in² of leather panels needed.
Practice Quiz
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