Final answer:
The most common map projections are based on three geometric shapes: the cylinder, the cone, and the plane. The cylinder is used for Mercator projections, which distort sizes as latitude increases. Any shape other than these three is not commonly used for map projections.
Step-by-step explanation:
The most common map projections are based on three geometric shapes, which are: the cylinder, the cone, and the plane. Map projections like the Mercator projection are based on a cylinder, meaning they project the globe onto a cylinder so that all the latitude lines have the same length as the equator. However, since the Earth is spherical, such cylindrical projections lead to distortions, especially near the poles where the map becomes increasingly stretched.
These distortions explain why on a Mercator projection map, regions such as Greenland or Antarctica appear significantly larger than they actually are when compared to equatorial regions. Due to the variation in shape, there could be many misconceptions about the true size of continents. For example, the True Size comparison shows that the United States, China, and India could all fit within the actual area of Africa with room to spare, whereas a Mercator map may suggest differently.
It is important to note that while these three shapes are most commonly used for map projections, there are numerous other ways earth's surface can be represented, each with its own set of compromises. Therefore, the correct answer to the student's question is that any geometric shape not among the cylinder, cone, or plane is not one of the three commonly used shapes for map projections.