Question

which statement about a sphere is true?
the great circle of a sphere is a three - dimensional circle.
the length of the diameter of a sphere is two times the length of the radius of the sphere.
the great circle of a sphere is not the same shape as the base of a cone.
the center of a sphere is created from a plane that passes through the sphere.

Explanation:

• A great - circle of a sphere is a two - dimensional circle (not three - dimensional), so the first statement is wrong.
• By the definition of diameter (\(d = 2r\)), the length of the diameter of a sphere is two times the length of the radius of the sphere, so the second statement is correct.
• The great - circle of a sphere and the base of a cone are both circles (two - dimensional), so the third statement is wrong.
• The center of a sphere is a point (not created from a plane passing through the sphere), so the fourth statement is wrong.

Answer:

The length of the diameter of a sphere is two times the length of the radius of the sphere.