Diagonally Halved Cylinder Calculator

Name: Diagonally Halved Cylinder - Geometry Calculator
Author: Jürgen Kummer

Calculations at a diagonally halved or bisected right circular cylinder. Hereby, such a cylinder is cut by a plane through two farthest points on the cylinder, in a way so that two equal parts emerge. These calculations refer to one of these two parts, while the other part is removed. The intersection area between the plane and the cylinder is an ellipse with semi-axes r and d/2. The diagonal d is the greatest length of this ellipse.
Enter cylinder radius and height and choose the number of decimal places. Then click Calculate.

Formulas:

d = \sqrt{h^{2} + {(2 \cdot r)}^{2}}

A = π \cdot r \cdot (h + r + \frac{d}{2})

L = π \cdot r \cdot h

V = \frac{π}{2} \cdot r^{2} \cdot h

pi:

π = 3.141592653589793...

Radius, height and diagonal 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. The lateral surface is the curved part of the surface area.

This diagonally bisected cylinder has a plane of symmetry perpendicular to the plane of intersection through the two farthest points. There are no other symmetries in this shape. The intersection of this plane of symmetry with the diagonally bisected cylinder is a right triangle with sides h and 2r and hypotenuse d. The lateral surface is the curved part of this shape, excluding the intersection of the ellipse, the circle of the base, as well as the interior. This lateral surface has a height between zero, or one point, up to h. At the point where its height is zero, it is not interrupted but is closed by exactly this one point, where circle and ellipse meet.

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