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Colony, protectorate, sphere of influence, and economic imperialism.
For a given area, the biggest volume you can enclose is a sphere. A sphere has the best volume-to-area ratio.
A sphere of influence is an area were foreign nations What_is_a_sphere_of_influencespecial rights and economic privileges.Read more: What_is_a_sphere_of_influence
The radius of a sphere is equal distance from the center of the sphere to all points within the sphere.
Sphere is one syllable: sphere.