A __________ of a sphere is the trace in its surface of the intersection of a plane passing through the center of the sphere.

• A. Small circle
• B. Circle of latitude
• C. Great circle
• D. Equator circle

Answer: (C)

When a plane cuts a sphere and passes through the sphere’s center, the curve where the plane meets the surface is a great circle. A great circle is a circle on the sphere whose center is the same as the sphere’s center, so its radius equals the sphere’s radius. The reason this trace is the best answer is that the intersecting plane contains the center, giving a cross-section with the largest possible radius, equal to the sphere’s. If the plane didn’t pass through the center, the cross-section would be a smaller circle (a small circle); a circle of latitude is another example of a small circle, except the equator is a great circle because it goes through the center.