\[V=\frac{\pi h}{6}\left(3a^2+3b^2+h^2\right)\]
Variables
Vspherical segment volume
hsegment height
alower base radius
bupper base radius
Description
What is this formula?
This formula calculates the volume of a spherical segment. A spherical segment is the portion of a sphere bounded between two parallel planes.
When to use it
Use this formula when determining the volume of sliced spherical sections, partially filled vessels, or geometric spherical zones.
Example
If the segment height is 4 m, the lower base radius is 3 m, and the upper base radius is 2 m:
V = π(4)(3×3² + 3×2² + 4²)/6
V ≈ 109.96 m³
Applications
- Geometry and mathematics
- Spherical tank calculations
- Mechanical engineering
- Industrial vessel design
- Fluid storage estimation
- Scientific modeling