pyramid

23 - Sphere cut into a pyramid

DiffCalc 020 Square pyramid inscribed in a sphere

Problem 23

A sphere is cut in the form of a right pyramid with a square base. How much of the material can be saved?

 

The Regular Tetrahedron

Solid 009 Regular Tetrahedron and its Face

Regular tetrahedron is one of the regular polyhedrons. It is a triangular pyramid all of whose faces are equilateral triangles.

 

Regular Pyramid

Solid 008 Regular Polygon and a Lateral Face

A regular pyramid is one whose base is a regular polygon whose center coincides with the foot of the perpendicular dropped from the vertex to the base.

 

The Pyramid

solid 007 Pyramid with a section parallel to the base

A pyramid is a polyhedron with a polygon base of any shape, and all other faces are triangles which have common vertex.

 

Solids for which Volume = 1/3 Area of Base times Altitude

solid 006 Pyramid and Cone

This is a group of solids in which the volume is equal to one-third of the product of base area and altitude. There are two solids that belong to this group; the pyramid and the cone.

 

66 - 68 Maxima and minima: Pyramid inscribed in a sphere and Indian tepee

DiffCalc 020 Square pyramid inscribed in a sphere

Problem 66

Find the largest right pyramid with a square base that can be inscribed in a sphere of radius a.

 

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