What is meant by the development of a surface?
Answer: A
Every element of the surface keeps its true length and every area its true size, so the flat pattern can be cut from sheet and folded up to the original form. It is the drawing a sheet-metal worker actually works from, which is why no dimension in it may be foreshortened.
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Which surfaces can be developed exactly?
Answer: B
A ruled surface such as a cylinder or cone can be unrolled because it is flat in one direction at every point. A surface curved both ways, of which the sphere is the standard case, cannot be flattened without stretching it somewhere.
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Why can a sphere not be developed exactly?
Answer: C
Double curvature means no part of it is flat in any direction, so flattening requires the material to stretch or tear. Approximate developments by zones or by lunes are used in practice, and every map projection is a version of the same compromise.
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Every line drawn on a development must be
Answer: D
Since the pattern will be cut and folded, a line short of its true length gives a piece that will not close. Obtaining true lengths for the oblique edges is therefore the substance of most development problems, and the reason auxiliary constructions appear in them.
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What does the lateral surface of a solid exclude?
Answer: A
Development of the lateral surface alone gives the wrapper, and the bases are drawn separately if they are needed. A sheet-metal pattern also carries seams and laps for joining, which are added outside the geometrical development.
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Which method suits the development of a prism or a cylinder?
Answer: B
Their generators are parallel and of equal length, so the pattern is set out on a straight stretch-out line with the generators erected perpendicular to it. A pyramid or cone instead has generators converging on an apex, which calls for the radial method.
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The radial line method is appropriate when a solid's generators
Answer: C
Convergence on a point makes that point the natural centre for the pattern, struck as a sector or a fan of triangles with the true slant length as radius. Using the vertical height as that radius instead is the commonest error in such a development.
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Which method is used for a transition piece joining a square duct to a round one?
Answer: D
The surface is divided into a series of triangles whose true sides are found individually, and the pattern is built by laying them out edge to edge. Neither parallel generators nor a common apex exists on such a surface, so neither simpler method applies.
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On what line are the generators of a cylinder erected in the parallel line method?
Answer: A
The base circle is divided into equal parts and those chord lengths are laid end to end along the straight line, which is why the total equals the circumference. Each generator is then erected at its own station to the height the solid has there.
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What radius is used to strike the arc of a cone's development?
Answer: B
Correct answer: the slant height of the cone
A development consists entirely of true lengths, and the true distance from apex to base rim along the surface is the slant height. The vertical height is the perpendicular from apex to base and lies inside the solid, so it appears nowhere on the surface and cannot bound the pattern.
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