Hemisphere — Volume + Surface Area
Hemisphere (half sphere): V = (2/3)πr³, curved SA = 2πr², total SA (with flat base) = 3πr².
Result
Volume
261.7994
(2/3)πr³ = 261.7994. Total SA (with base) = 235.6194.
- Radius5
- Volume ((2/3)πr³)261.799388
- Curved SA (2πr²)157.079633
- Flat base area (πr²)78.539816
- Total SA (3πr²)235.619449
Step-by-step
- V = (2/3)πr³ = (2/3) × π × 5³ = 261.7994. (Half a full sphere.)
- Curved SA = half the sphere = ½ × 4πr² = 2πr² = 157.0796.
- Flat base = πr² = 78.5398.
- Total SA = curved + base = 157.0796 + 78.5398 = 235.6194.
How to use this calculator
- Enter radius.
- Read volume; pick curved-only SA (dome) or total SA (dome + base) per use case.
About this calculator
A hemisphere is exactly half of a sphere, cut by a plane through the center. Volume V = (2/3)πr³ — half of (4/3)πr³. The curved (dome) surface is half the full sphere's surface = 2πr². If you include the flat circular base (the cut face), total SA = 2πr² + πr² = 3πr². Common in domes, half-pipes, lenses, and zero-gravity liquid surfaces. Source: Apostol, "Calculus" Vol II §10; Larson Ch. 11.
Frequently asked
Curved = the dome surface (2πr²). Total = dome + the flat circular base (3πr²). Painting a half-orange skin: curved. Building a dome with a floor: total.
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