sphere

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?

 

22 - Smallest cone that may circumscribe a sphere

MaxMin 22 Sphere inside a conical vessel

Problem 22

A sphere of radius a is dropped into a conical vessel full of water. Find the altitude of the smallest cone that will permit the sphere to be entirely submerged.

 

03 - Heaviest cylinder that can be made from a shot

MaxMin 02 - Cylinder inscribed in a sphere

Problem 3

Find the weight of the heaviest circular cylinder can be cut from a 16-lb shot.

 

02 - Cylinder of maximum convex area inscribed in a sphere

MaxMin 02 - Cylinder inscribed in a sphere

Problem 02

A cylinder is inscribed in a given sphere. Find the shape of the cylinder if its convex surface area is a maximum.

 

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.

 

64 - 65 Maxima and minima: cone inscribed in a sphere and cone circumscribed about a sphere

Problem 64

A sphere is cut to the shape of a circular cone. How much of the material can be saved? (See Problem 63)

 

62 - 63 Maxima and minima: cylinder inscribed in a cone and cone inscribed in a sphere

DiffCalc 019 Cylinder inscribed in a cone

Problem 62

Inscribe a circular cylinder of maximum convex surface area in a given circular cone.

 

29 - 31 Solved problems in maxima and minima

DiffCalc 007 Lenght and girth of a container with square cross-section

Problem 29

The sum of the length and girth of a container of square cross section is a inches. Find the maximum volume.

 

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