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.
Problem 3 Find the weight of the heaviest circular cylinder can be cut from a 16-lb shot.
Problem 02 A cylinder is inscribed in a given sphere. Find the shape of the cylinder if its convex surface area is a maximum.
Problem 66 Find the largest right pyramid with a square base that can be inscribed in a sphere of radius a.
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 62 Inscribe a circular cylinder of maximum convex surface area in a given circular cone.
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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