Spherical Cap Volume
Spherical Cap Volume
\[V=\frac{\pi h^2(3r-h)}{3}\]
Variables
V = spherical cap volume
r = sphere radius
h = cap height
Description
What is this formula?
This formula calculates the volume of a spherical cap. A spherical cap is the portion of a sphere cut off by a plane.
When to use it
Use this formula when determining the volume of partially filled spherical tanks, domes, lenses, or cut spherical sections.
Example
If a sphere has a radius of 5 m and the cap height is 2 m:
V = π(2)^2(3×5−2)/3
V ≈ 54.45 m³
Applications
- Geometry and mathematics
- Storage tank calculations
- Mechanical engineering
- Dome and lens design
- Fluid volume estimation
- Industrial process engineering
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