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.
60 - 61 Maxima and minima problems of a folded page
Problem 60
One corner of a leaf of width a is folded over so as just to reach the opposite side of the page. Find the width of the part folded over when the length of the crease is a minimum. See Figure 41.
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58 - 59 Maxima and minima: cylinder surmounted by hemisphere and cylinder surmounted by cone
Problem 58
For the silo of Problem 57, find the most economical proportions, if the floor is twice as expensive as the walls, per unit area, and the roof is three times as expensive as the walls, per unit area.
56 - 57 Maxima and minima problems of square box and silo
Problem 56
The base of a covered box is a square. The bottom and back are made of pine, the remainder of oak. If oak is m times as expensive as pine, find the most economical proportion.
53 - 55 Solved Problems in Maxima and Minima
Problem 53
Cut the largest possible rectangle from a circular quadrant, as shown in Fig. 40.
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50 - 52 Nearest distance from a given point to a given curve
Problem 50
Find the shortest distance from the point (4, 2) to the ellipse x2 + 3y2 = 12.
48 - 49 Shortest distance from a point to a curve by maxima and minima
Problem 48
Find the shortest distance from the point (5, 0) to the curve 2y2 = x3.
46 - 47 Solved Problems in Maxima and Minima
Problem 46
Given point on the conjugate axis of an equilateral hyperbola, find the shortest distance to the curve.
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