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Which surfaces can be developed exactly?

  • A.only those bounded entirely by plane faces
  • B.those generated by a straight line moving along a path
  • C.those curved in two directions at once
  • D.any surface whatever, given a fine enough subdivision

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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