## 02 - Cylinder of maximum convex area 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

Problem 66
Find the largest right pyramid with a square base that can be inscribed in a sphere of radius a.

Problem 67
An Indian tepee is made by stretching skins or birch bark over a group of poles tied together at the top. If poles of given length are to be used, what shape gives maximum volume?

## 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).

Problem 65
Find the circular cone of minimum volume circumscribed about a sphere of radius a.

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

Problem 62
Inscribe a circular cylinder of maximum convex surface area in a given circular cone.

Problem 63
Find the circular cone of maximum volume inscribed in a sphere of radius a.

## 29 - 31 Solved problems in maxima and minima

Problem 29
The sum of the length and girth of a container of square cross section is a inches. Find the maximum volume.

Problem 30
Find the proportion of the circular cylinder of largest volume that can be inscribed in a given sphere.

Problem 31
In Problem 30 above, find the shape of the circular cylinder if its convex surface area is to be a maximum.

## 36 Review Problem - Circular hole bored through a sphere

Problem 36
A hole 6 in. in diameter was bored through a sphere 10 in. in diameter. Find the volume of the part cut out.

## 34 Review Problem - Sphere dropped into a cone

Problem 34
The inside of a vase is an inverted cone 2.983 in. across the top and 5.016 in. deep. If a heavy sphere 2.498 in. in diameter is dropped into it when the vase is full of water, how much water will overflow?