Work out sphere volume instantly with clear inputs, formula shown and shareable results.
Archimedes showed that a sphere occupies two thirds of its circumscribing cylinder, which gives V = ⁴⁄₃πr³. The surface area 4πr² is exactly the derivative of the volume with respect to r.
Volume
V = ⁴⁄₃πr³
Surface area
S = 4πr²
⁴⁄₃π × 216 = 288π ≈ 904.778684 cubic units.
Growing the radius by dr adds a thin shell of thickness dr over the whole surface, so the added volume is S·dr.