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**Hint:**A map projection is a way to flatten a globe's surface into a plane in order to make a map. This requires a standardized conversion of the latitudes and longitudes of locations from the surface of the globe into locations on a plane.

**Complete answer:**

Looking at the above options:

a.Cylindrical projection is a map projection in which the surface characteristics of a globe are illustrated as if projected onto a cylinder commonly positioned with the globe centered horizontally inside the cylinder. The most famous map projection, the Mercator, is a cylindrical projection. This option is incorrect.

b. Conic projection is a map projection in which the surface characteristics of a globe are portrayed as if projected onto a cone commonly placed so as to rest on the globe along a parallel. This option is incorrect.

c.An equal area projection is a map projection that shows regions of the same size on the Earth, the same size on the map but may distort the shape, angle or scale. An equal area map conserves the ratio of mapped area to the corresponding earth area. To conserve equality between a given area shown on a flat surface, the shape must be compromised. Most equal-area projection is mathematically originated. This option is correct.

d. The azimuthal projection has the useful properties that all points on the map are at proportionally correct distances from the center point. This option is incorrect.

**Hence, The correct answer is Option c.**

**Note:**- The equal area projection shows the correct sizes of landmasses and continents.

- The disadvantage of such maps is that it causes the shapes of landmasses to be altered and forced into curves.

- Equal-area maps are also called equivalent or authalic.

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