Question

in the diagram, point c represents the center of the sphere. diego says that the part of the sphere labeled d is the radius. gregoire says that the part of the sphere labeled d is the diameter of the sphere. who is correct and why? gregoire is correct; the diameter is a chord that passes through the center of the sphere. gregoire is correct; the diameter is a chord that is from the center to the surface of the sphere. diego is correct; the radius is a chord that is from the center to the surface of the sphere. diego is correct; the radius is a chord that passes through the center of the sphere.

Explanation:

Step1: Recall definitions

• Radius: A line segment from the center of a sphere to its surface.
• Diameter: A chord (a line segment connecting two points on the sphere's surface) that passes through the center of the sphere.

Step2: Analyze Diego's and Gregoire's statements

• Gregoire says the part labeled \(D\) (the dashed line passing through the center \(C\)) is the radius. But the radius is from the center to the surface (shorter line - not shown in full in the definition of \(D\) here).
• Gregoire is wrong. The part labeled \(D\) is a chord (connects two points on the sphere's surface) that passes through the center. By the definition of diameter (a chord passing through the center), Gregoire is incorrect in calling it a radius.
• The diameter is a chord that passes through the center of the sphere.

Answer:

Gregoire is correct; the diameter is a chord that passes through the center of the sphere.