Cylinder (EntityTopic, 14)

From Hi.gher. Space

Revision as of 18:20, 24 November 2009

A cylinder is a special case of a prism where the base is a circle.

Equations

• Variables:

r ⇒ radius of cylinder
h ⇒ height of cylinder

• All points (x, y, z) that lie on the surface of a cylinder will satisfy the following equations:

x² + y² = r²
abs(z) ≤ h/2
   -- or --
x² + y² < r²
abs(z) = h/2

• All points (x, y, z) that lie on the edges of a cylinder will satisfy the following equations:

x² + y² = r²
abs(z) = h/2

• The hypervolumes of a cylinder are given by:

total edge length = 4πr
surface area = 2πr(r+h)
volume = πr²h

• The planar cross-sections (n) of a cylinder are:

[!x,!y] ⇒ rectangle with width (2rcos(πn/2)), height (h)
[!z] ⇒ circle of radius (r)

Cylindrogram

A cylindrogram is the surface of revolution of a parallelogram, just as a cylinder is the surface of revolution of a rectangle. It can also be thought of as a cylinder with a cone removed from one end and placed on the other. As such, this shape has the same volume as a cylinder with the same radius and height.