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The sphere that we all live on is called the Earth. (It is not a perfect sphere, but close enough)
We live on a sphere. Calculating 'shortest' distance on the sphere is not a simple trig problem, you may need spherical trig.
The earth, which we live on, is approximately a sphere. It is important, therefore, to know spherical trigonometry.
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.