Welcome to Sphere Geometry!
Let's Explore 3D Shapes!
Spheres are perfect 3D shapes all around us - from balls to planets! Choose a lesson below to start your mathematical journey!
📚 Key Theory Concepts
What is a Sphere?
A sphere is a 3D shape where every point on its surface is equidistant from the center point.
- No edges or vertices
- Perfectly round in all directions
- Only one curved surface
Surface Area Formula
Surface Area = 4πr²
Where:
- r = radius of the sphere
- π ≈ 3.14159 (or 22/7)
Hemisphere Formulas
Curved Surface Area:
CSA = 2πr²
Total Surface Area:
TSA = 3πr²
Includes the flat circular base
Key Properties
- Surface area grows quadratically with radius
- Doubling radius = 4× surface area
- Sphere has maximum volume for given surface area
- Hemisphere CSA = ½ of sphere surface area
Quick Calculations
Common Values:
- r = 1 → SA = 4π ≈ 12.57
- r = 2 → SA = 16π ≈ 50.27
- r = 3 → SA = 36π ≈ 113.10
- r = 7 → SA = 196π ≈ 615.75
Remember This!
- Always use radius, not diameter
- If given diameter, divide by 2 first
- Surface area units are square units
- Hemisphere has 2 types of surface area
- Sphere surface = 4 × circle area