# Sphere

## 22 - Smallest cone that may circumscribe a sphere

## 03 - Heaviest cylinder that can be made from a shot

**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

**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.

## 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

**Problem 62**

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

## 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.

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