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Why can a sphere not be developed exactly?

  • A.it has no straight generators of finite length
  • B.its radius varies from one point to another
  • C.it is curved in two directions at every point
  • D.its surface area cannot be calculated in closed form

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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