Calculations in a paraboloid of revolution (an elliptic paraboloid with a circle as top surface). This is defined by a parabolic segment based on a parabola of the form y=sx² in the interval x ∈ [ -a ; a ], that rotates around its height. Enter the shape parameter s (s>0, normal parabola s=1) and the maximal input value a (equivalent to the radius) and choose the number of decimal places. Then click Calculate.
h = s * a²
L = π * a / ( 6 * h² ) * [ ( a² + 4h² )3/2 - a³ ]
A = L + π * a²
V = 1/2 π * a² * h
π = 3.141592653589793...
The shape parameter has no unit, radius a and height have the same unit (e.g. meter), lateral and surface area have this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). A/V has this unit -1.