Calculations at a double calotte. A double calotte is a spherical cap, with a height smaller than the radius of the sphere, with another spherical cap of the same size attached at their flat sides. The double calotte ist the intersection of the double sphere.
Enter radius of the sphere and height of the double calotte and choose the number of decimal places. Then click Calculate.
Formulas:
b = 2 * √ h/2 * ( 2r - h/2 )
A = 2 * π * r * h
V = h² * π/6 * ( 3r - h/2 )
pi:
π = 3.141592653589793...
Radius, height and width have the same unit (e.g. meter), the area has 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.
A double calotte is the same as a double spherical segment, yet the calotte is different from a spherical segment, namely it is only the curved part of its surface. However, the flat part of the surface of the spherical segment is no longer a surface when this is doubled, because the two parts are joined exactly there.
The double calotte has a plane of symmetry along its single, circular edge. It has an infinite number of other planes of symmetry, which pass through two opposite points on the edge and through the two points on the surface that is intersected by the axis of rotation. This axis of rotation runs from the center of the double calotte to the two points farthest from the edge plane. This makes the double calotte a solid of revolution.
If you insert a matching cylinder into the double calotte between the two spherical segments, you get a special case of a lens. A similar shape to the double calotte, based not on spherical segments but on half spheroids, is the egg shape. However, this shape has no edge. Of course, there would also be such a shape made of spheroid segments possible, which would have an edge, but this shape cannot be calculated algebraically.
