Circles and PiSphere Maps
Surface Area of a Sphere
Finding a formula for the surface area of a sphere is very difficult. One reason is that we can’t open and “flatten” the surface of a sphere, like we did for cones and cylinders before.
This is a particular issue when trying to create maps. Earth has a curved, three-dimensional surface, but every printed map has to be flat and two-dimensional. This means that Geographers have to cheat: by stretching or squishing certain areas.
Here you can see few different types of maps, called projections. Try moving the red square, and watch what this area actually looks like on a globe: