Calculations at a cylindrical wedge. A cylindrical wedge is a cylinder, which is inclined cropped in a way that it is cut through the base. Otherwise it is a cut cylinder. The shape between the cylindrical wedge and the cut cylinder is the diagonally halved cylinder, which can be seen as either one or the other shape.
Enter radius of the cylinder, height and angle and choose the number of decimal places. Then click Calculate. Angles are calculated and displayed in degrees, here you can convert angle units.
The angle Φ must be in the interval ]0°; 180°]. At 180°, the cut touches the base without hurting it. At 90°, the base gets bisected.
Formulas:
Φ ≥ 90°: l = r + √ r² - r² * sin²(Φ)
Φ < 90°: l = r - √ r² - r² * sin²(Φ)
L = { 2 * h * r * [ sin(Φ) - Φ * cos(Φ) ] } / [ 1 - cos(Φ) ]
V = h * r² * [ 3 * sin(Φ) - 3 * Φ * cos(Φ) - sin³ (Φ) ] / { 3 * [ 1 - cos(Φ) ] }
Radius, length and height have the same unit (e.g. meter), the lateral surface has this unit squared (e.g. square meter), the volume has this unit to the power of three (e.g. cubic meter). The lateral surface is the curved part of the surface area. The lower plane is a circular segment with Θ = 2 * (180° - Φ), for the calculation see there. The upper plane is an elliptic segment. Calculating this is complicated.
A wedge generally describes a shape in which two flat sides meet at an acute angle. This angle can be calculated from the properties of a right triangle with legs h and l; it is the opposite angle of leg h. The line between the ends of h and l is the hypotenuse of this right triangle.
This right triangle also forms the plane of symmetry to which the cylindrical wedge is mirror-symmetric. This shape has no other symmetries.
The counterpart of this shape, a cylinder from which a wedge has been cut, has of course the volume of the original cylinder minus that of the cylindrical wedge.
