Comparing Spheres and Hemispheres
A hemisphere is created by bisecting a sphere along any plane that passes through its geometric center. While calculating volume is straightforward (exactly half), calculating surface area requires careful attention to whether the hemisphere is hollow or solid.
Mathematical Formula Comparison
| Property | Full Sphere | Solid Hemisphere | Hollow Hemisphere |
|---|---|---|---|
| Volume (V) | 4/3 π r³ | 2/3 π r³ | 2/3 π (r_outer³ - r_inner³) |
| Curved Area | 4 π r² | 2 π r² | 2 π r² |
| Base Disc Area | None (0) | π r² | None (open) |
| Total Area | 4 π r² | 3 π r² | 2 π r² |