Q: What is a system for mapping the round earth on a flat surface called!?

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It is called a landform.

They project the surface of a sphere (the Earth) using a projection. Often the latitudes and longitudes are mapped onto the coordinate plane for small area but such projections distort shapes when mapping larger areas.

A globe or a sphere perhaps?

The surface area pf the Earth is on a sphere, not a flat surface.

Lets pretend that the Earth is a perfect sphere. Surface area of a sphere = 4(pi)(radius)^2. The radius of earth is 6378.1 km. Plug that into your equation and you'll get your answer.

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Its called a projection map

Its called a projection map

projection map

A system of mapping the round earth on a flat surface is called a map projection. Map projections are used to represent the Earth's curved surface on a two-dimensional map. Different map projections have different strengths and weaknesses depending on the purpose of the map.

GPS

It is known as cartography.

Cartography or Geodesy .

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