Kalkulator Objętości Kuli

Sphere Geometry & Derivation

A sphere is defined as the set of all points in three-dimensional space equidistant from a central point. The distance from the center to any surface point is the radius r.

Key Mathematical Formulas

1. Volume (V): V = (4/3) × π × r³ = (π × d³) / 6

2. Surface Area (A): A = 4 × π × r² = π × d²

3. Circumference (C): C = 2 × π × r = π × d

4. Hollow Spherical Shell Volume: V_shell = (4/3) × π × (R_outer³ - r_inner³)

Spherical tank – calculation example

Let’s calculate the volume of a spherical gas storage pressure vessel with diameter 10 meters (radius 5 meters):

1. Spherical radius: radius = 5 m.
2. Compute surface area: surface area = 314.16 m².
3. The calculation results are available for you: tank volume = 523.60 m³ (138,322 US gallons / 523,598 Liters).
4. Circumference around equator: circumference = 31.42 m.

💡 Archimedes proved in 225 BC that a sphere possesses exactly two-thirds the volume and surface area of a cylinder enclosing it with diameter and height equal to 2r.