Calculating the Volume of a Hemisphere
Because a hemisphere is formed by cutting a sphere into two identical halves, its volume is exactly one-half of a complete sphere:
V_hemisphere = (1/2) × (4/3 π r³) = 2/3 × π × r³
Dome Architecture Example
A planetarium dome is built in the shape of a hemisphere with internal radius r = 12 meters. What volume of air does it contain?
V = 2/3 × π × (12)³ = 2/3 × π × 1728 = 1152π ≈ 3,619.11 m³