Which of the following is true about the Diameter of a sphere
the diameter of a sphere passes through the center of the circle
the diameter is not a chord
the diameter is 2.5 times the length of the radius
the diameter is the shortest length on a sphere
Let's examine each statement to determine which is true about the diameter of a sphere:
1. "the diameter of a sphere passes through the center of the circle":
- This is partially true but slightly misstated, as the correct term should be "sphere" rather than "circle." A diameter of a sphere is indeed a line segment that passes through the center of the sphere and has its endpoints on the sphere's surface.
2. "the diameter is not a chord":
- This statement is false. A diameter is a special case of a chord. In a circle or sphere, a chord is a line segment with both endpoints on the sphere's surface. The diameter is the longest possible chord in a sphere, passing through the center of the sphere.
3. "the diameter is 2.5 times the length of the radius":
- This statement is false. The diameter of a sphere is exactly twice the length of the radius (D = 2r).
4. "the diameter is the shortest length on a sphere":
- This statement is false. The diameter is the longest straight line you can draw within a sphere, not the shortest. The shortest length between two points on a sphere's surface is not a straight line through the interior of the sphere, but rather an arc along the surface, which is part of a great circle.
The correct statement about the diameter of a sphere is therefore the first one, with the term "circle" replaced with "sphere." To summarize, the diameter of a sphere passes through the center of the sphere, is a special case of a chord, is twice the length of the radius, and is the longest straight line segment that fits entirely inside the sphere.
Just choose one
Apologies for any confusion. If I have to choose one statement that is true about the diameter of a sphere, it would be:
"The diameter of a sphere passes through the center of the sphere."
(Note: I've corrected "circle" to "sphere" to make the statement accurate.)
To determine which of the statements about the diameter of a sphere is true, let's go through each option:
1. The diameter of a sphere passes through the center of the circle:
This statement is true. The diameter of a sphere is a line segment that passes through the center point of the sphere and has its endpoints on the sphere's surface.
2. The diameter is not a chord:
This statement is also true. A chord is a line segment that connects two points on a circle's circumference. However, the diameter is a specific type of chord that passes through the center of the circle.
3. The diameter is 2.5 times the length of the radius:
This statement is not true. The diameter of any sphere is always exactly twice the length of its radius. So the correct statement would be that the diameter is two times the length of the radius, not 2.5 times.
4. The diameter is the shortest length on a sphere:
This statement is false. The diameter of a sphere is actually the longest possible straight-line distance that can be drawn on the sphere, as it passes through the center and connects two points on the surface.
In conclusion, option 1 and option 2 are true about the diameter of a sphere, while option 3 and option 4 are not true.