Which three-dimensional figure consists of all points at a fixed distance from a center?

• A. Cone
• B. Cylinder
• C. Cube
• D. Sphere

Answer: (D)

The key idea is the locus of points that are all the same distance from a single point. When every point is exactly a fixed distance from the center, you get a sphere—the surface enclosing a ball. This shape is defined by that constant distance, or radius, from the center in every direction.

A cone or cylinder are built around an axis or a vertex and don’t have all points the same distance from one center. A cube also contains points at many different distances from any given center due to its corners, edges, and faces. Therefore, the figure formed by all points at a fixed distance from the center is a sphere.