Calculations at an intersection of sphere and cylinder. The cylinder goes straight through the center of the sphere and the cylinder radius must be smaller than the sphere radius. This means spherical caps are attached to the cylinder. The domed surfaces of these spherical caps are so called calottes. These are the ends of the sphere cylinder intersection that were previously part of the spherical surface. The length of the original cylinder must be greater than the diameter of the sphere, but is otherwise irrelevant.
Enter the radius of the sphere and of the cylinder and choose the number of decimal places. Then click Calculate.
Formulas:
h = r - √ 4 * r² - 4 * a² / 2
l = 2 * r
m = l - 2 * h
d = 2 * a
AK = 2 * π * r * h
A = 2 * π * a * m + 2 * AK
V = π * a² * m + 2 * h² * π / 3 * ( 3 * r - h )
pi:
π = 3.141592653589793...
Radiuses, height, lengths and diameter have the same unit (e.g. meter), the area has 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.
If a sphere cylinder intersection is cut out of a cylinder, a spherical ring remains as the residue. A related shape to the sphere cylinder intersection is the capsule, which has hemispheres attached to it instead of spherical caps. A sphere cylinder intersection can never also be a spherical capsule.
The sphere cylinder intersection has the same symmetry properties as the right circular cylinder. It is therefore rotationally symmetric about the axis of rotation running along the center of the cylinder and its two spherical segments. Along this axis of rotation, it has infinitely many planes of symmetry that rotate with it. Another plane of symmetry passes perpendicularly through the center of the cylinder. The sphere cylinder intersection is point-symmetric about its center point, which lies at the intersection of the axis of rotation and the perpendicular plane of symmetry.