14-15 Ladder reaching the house from the ground outside the wall
Problem 14
A wall 10 ft high is 8 ft from the house. Find the length of the shortest ladder that will reach the house, when one end rests on the ground outside the wall.
13 - Sphere cut into a circular cone
Problem 13
A sphere is cut in the shape of a circular cone. How much of the material can be saved?
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12 - Cone of maximum convex area inscribed in a sphere
Problem 12
Find the altitude of the circular cone of maximum convex surface inscribed a sphere of radius a.
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11 - Triangular gutter of maximum carrying capacity
Problem 11
A gutter having a triangular cross-section is to be made by bending a strip of tin in the middle. Find the angle between the sides when the carrying capacity is to a maximum.
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10 - Largest conical tent of given slant height
Problem 10
Find the largest conical tent that can be constructed having a given slant height.
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06-09 Trapezoidal gutter of greatest capacity
Problem 06
A trapezoidal gutter is to be made, from a strip of metal 22 inches wide by bending up the edges. If the base is 14 inches wide, what width across the top gives the greatest carrying capacity.
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04-05 Stiffness and strength of timber beam
Problem 4
The stiffness of a rectangular beam is proportional to the breadth and the cube of the depth. Find the shape of the stiffest beam that can be cut from a log of a given size.
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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.
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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.
01 Rectangle of maximum perimeter inscribed in a circle
Problem 01
Find the shape of the rectangle of maximum perimeter inscribed in a circle.
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