Cone (EntityTopic, 11)
From Hi.gher. Space
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*The [[hypervolume]]s of a cone are given by: | *The [[hypervolume]]s of a cone are given by: | ||
<blockquote>total edge length = 2π''r''<br> | <blockquote>total edge length = 2π''r''<br> | ||
| - | surface area = π''r'' | + | surface area = π''r''(''r'' + √(''r''<sup>2</sup> + ''h''<sup>2</sup>))<br> |
| - | volume = π''r''<sup>2</sup>''h'' | + | volume = {{Over|π|3}} · ''r''<sup>2</sup>''h''</blockquote> |
*The [[planar]] [[cross-section]]s (''n'') of a cone are: | *The [[planar]] [[cross-section]]s (''n'') of a cone are: | ||
<blockquote>[!x,!y] ⇒ ''Unknown''<br> | <blockquote>[!x,!y] ⇒ ''Unknown''<br> | ||
| - | [!z] ⇒ circle of radius (''r'' | + | [!z] ⇒ circle of radius (''r'' − ''rnh''<sup>-1</sup>)</blockquote> |
== Arrinder == | == Arrinder == | ||
Revision as of 12:28, 18 November 2011
A cone is a special case of a pyramid where the base is a circle.
The cone is one of the few curved polyhedra that satisfy Euler's F + V = E + 2.
Equations
- Variables:
r ⇒ radius of base of cone
h ⇒ height of cone
- All points (x, y, z) that lie on the surface of a cone will satisfy the following equations:
Unknown
- All points (x, y, z) that lie on the edges of a cone will satisfy the following equations:
x2 + y2 = r2
z = 0
- The hypervolumes of a cone are given by:
total edge length = 2πr
surface area = πr(r + √(r2 + h2))
volume = π∕3 · r2h
- The planar cross-sections (n) of a cone are:
[!x,!y] ⇒ Unknown
[!z] ⇒ circle of radius (r − rnh-1)
Arrinder
An arrinder is the surface of revolution of an arrow, just as a cone is the surface of revolution of a triangle. It can also be thought of as a cone with a smaller cone removed from the base. As such, this shape's volume is the difference between the volume of the two aforementioned cones.
| Notable Trishapes | |
| Regular: | tetrahedron • cube • octahedron • dodecahedron • icosahedron |
| Direct truncates: | tetrahedral truncate • cubic truncate • octahedral truncate • dodecahedral truncate • icosahedral truncate |
| Mesotruncates: | stauromesohedron • stauroperihedron • stauropantohedron • rhodomesohedron • rhodoperihedron • rhodopantohedron |
| Snubs: | snub staurohedron • snub rhodohedron |
| Curved: | sphere • torus • cylinder • cone • frustum • crind |
| 7. 111 Cube | 8. 21 Cone | 9. [11]1 Square pyramid |
| List of tapertopes | ||
