Which of the following is a solid bounded by the set of all points at a given distance from a given point?A.ConeB.SphereC.CubeD.Cylinder

Step 1: Break Down the Problem

We need to identify the solid that is defined as the set of all points at a given distance from a specific point.

Step 2: Relevant Concepts

• The definition of a sphere: A sphere is the collection of all points in three-dimensional space that are equidistant from a fixed point (the center).
• The definitions of the other options:
  • A cone is a solid with a circular base that tapers to a point (vertex).
  • A cube is a three-dimensional shape with six square faces.
  • A cylinder is a three-dimensional shape with two circular bases connected by a curved surface.

Step 3: Analysis and Detail

To determine which option fits the definition best:

1. Sphere: A sphere is defined precisely as the set of all points in space that are a fixed distance (radius) away from a center point.
2. Cone: Does not satisfy the condition; points are not all at the same distance from the vertex.
3. Cube: Also does not match; only specific points are at a fixed distance from the center.
4. Cylinder: Again, does not meet the requirement since it contains points at varying distances from its axis.

Step 4: Verify and Summarize

Among the options, only the sphere meets the criterion of being the solid bounded by the set of all points at a given distance from a given point.

Final Answer

B. Sphere is the solid bounded by the set of all points at a given distance from a given point.