Share on Facebook Share on Twitter Email
Answers.com

Pyramid

 

A pointed or cone-shaped structure or part.

  • p. breed structure — a standard format for a multiple herd system comprising a breed structure; headed by an open or closed nucleus, a second tier of multiplier herds and a terminal tier of commercial herds which produce the end-product to be marketed. The nucleus, perhaps one herd, produces all of the basic genetic material and supplies breeding stock to the multiplier herds which have the prime role of multiplying the progeny for supply to commercial herds who produce the end product. The entire system is under the control of one organization. Ideally suited to the pig industry.
  • p. of cerebellum — pyramid of vermis.
  • p. of light — a triangular reflection seen upon the tympanic membrane.
  • malpighian p's — renal pyramids.
  • p's of the medulla oblongata — either of two rounded masses, one on either side of the median fissure of the medulla oblongata.
  • renal p's — the conical masses constituting the medulla of certain kidneys, the base toward the cortex and culminating at the summit in the renal papilla.
  • p. of tympanum — the hollow elevation in the inner wall of the middle ear that contains the stapedius muscle.
  • p. of vermis — the part of the vermis cerebelli between the tuber vermis and the uvula.
Search unanswered questions...
Enter a question here...
Search: All sources Community Q&A Reference topics
Wikipedia: Pyramid (geometry)
Top
Set of pyramids
Square Pyramid
Faces n triangles,
1 n-gon
Edges 2n
Vertices n + 1
Symmetry group Cnv
Dual polyhedron Self-dual
Properties convex
The 1-skeleton of pyramid is a wheel graph
This article is about the polyhedron pyramid (a 3-dimensional shape); for other versions including architectural pyramids, see Pyramid (disambiguation).

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Each base edge and apex form a triangle. It is a conic solid with polygonal base.

An n-sided pyramid will have n + 1 vertices, n + 1 faces, and 2n edges. All pyramids are self-dual.

When unspecified, the base is usually assumed to be square.

If the base is a regular polygon and the apex is above the center of the polygon, an n-gonal pyramid will have Cnv symmetry.

Pyramids are a subclass of the prismatoids.

Contents

Pyramids with regular polygon faces

The regular tetrahedron, one of the Platonic solids, is a triangular pyramid all of whose faces are equilateral triangles. Besides the triangular pyramid, only the square and pentagonal pyramids can be composed of regular convex polygons, in which case they are Johnson solids.

Tetrahedron Square pyramid Pentagonal pyramid
Tetrahedron.svg Square pyramid.png Pentagonal pyramid.png

Star pyramids

Pyramids with regular star polygon bases are called star pyramids. For example, the pentagrammic pyramid has a pentagram base and 5 intersecting triangle sides.

Pentagram pyramid.png

Volume

The volume of a pyramid is V= \tfrac{1}{3}Bh where B is the area of the base and h the height from the base to the apex. This works for any location of the apex, provided that h is measured as the perpendicular distance from the plane which contains the base.

The formula can be formally proved using calculus: By similarity, the dimensions of a cross section parallel to the base increase linearly from the apex to the base. Then, the cross section at any height y is the base scaled by a factor of 1 - \tfrac{y}{h}, where h is the height from the base to the apex. Since the area of any shape is multiplied by the square of the shape's scaling factor, the area of a cross section at height y is \frac{A(h - y)^2}{h^2}. The volume is given by the integral

\frac{A}{h^2} \int_0^h (h-y)^2 \, dy = \frac{-A}{3h^2} (h-y)^3 \bigg|_0^h = \tfrac{1}{3}Ah.

The volume of a pyramid whose base is a regular n-sided polygon with side length s and whose height is h is therefore:

V = \frac{n}{12}hs^2 \cot\frac{\pi}{n}.

The volume of a pyramid whose base is a regular n-sided polygon with radius R is therefore:

V = \frac{nR^2h}{6} \sin{\frac{2\pi}{n}}.

This property can be used to derive the volume for cones, as well. See also cone.

Surface area

The surface area of a pyramid is A= B + \frac{PL}{2} where B is the base area, P is the base perimeter and L is the slant height.

See also

External links


 
 
Learn More
pyramidion
pyramis
pyramidally

What was in the pyramids? Read answer...
What are pyramids? Read answer...
What is the pyramid for? Read answer...

Help us answer these
What is in pyramids?
How do you get out of the pyramids?
What is the pyramids from?

Post a question - any question - to the WikiAnswers community:

 

Copyrights:

Veterinary Dictionary. Saunders Comprehensive Veterinary Dictionary 3rd Edition. Copyright © 2007 by D.C. Blood, V.P. Studdert and C.C. Gay, Elsevier. All rights reserved.  Read more
Wikipedia. This article is licensed under the Creative Commons Attribution/Share-Alike License. It uses material from the Wikipedia article "Pyramid (geometry)" Read more