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.
A sphere. C is the center and D is the diameter.
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 passes through the center of the sphere.
Diego is correct; the radius is a chord that is from the center to the surface of the sphere.
A sphere. C is the center and D is the diameter.
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 passes through the center of the sphere.
Diego is correct; the radius is a chord that is from the center to the surface of the sphere.
Answers
GPT-4o mini
In the context of a sphere:
- The **radius** is defined as the distance from the center of the sphere (point C) to any point on the surface of the sphere. This would represent the length of a line segment extending from point C to the surface.
- The **diameter** is defined as the distance across the sphere, passing through the center. It is equal to twice the radius and can be represented as a chord that connects two points on the surface of the sphere while passing through the center.
Given Diego's statement about D being the radius and Gregoire's statement about D being the diameter, the following is true:
- If D refers to the distance from C to the surface of the sphere, then Diego is correct.
- If D refers to the distance across the sphere through C, then Gregoire is correct.
Since the problem states that Gregoire claims D is the diameter—this means that D would be a distance across the sphere. Therefore, the correct answer would be:
**Gregoire is correct; the diameter is a chord that passes through the center of the sphere.**
If D refers specifically to the segment from C to the surface, Diego would be correct. However, based on the nature of the statements, Gregoire's definition as the diameter is what would typically be considered based on the description.
- The **radius** is defined as the distance from the center of the sphere (point C) to any point on the surface of the sphere. This would represent the length of a line segment extending from point C to the surface.
- The **diameter** is defined as the distance across the sphere, passing through the center. It is equal to twice the radius and can be represented as a chord that connects two points on the surface of the sphere while passing through the center.
Given Diego's statement about D being the radius and Gregoire's statement about D being the diameter, the following is true:
- If D refers to the distance from C to the surface of the sphere, then Diego is correct.
- If D refers to the distance across the sphere through C, then Gregoire is correct.
Since the problem states that Gregoire claims D is the diameter—this means that D would be a distance across the sphere. Therefore, the correct answer would be:
**Gregoire is correct; the diameter is a chord that passes through the center of the sphere.**
If D refers specifically to the segment from C to the surface, Diego would be correct. However, based on the nature of the statements, Gregoire's definition as the diameter is what would typically be considered based on the description.