Q: What is the set of points in a space that are a given distance from a given point?

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The set of all points in space that are the same distance from a given point is called a sphere.

A spherical surface, with its center at the given point, and its radius equal to the given distance.

surface area of a cylinder? No. In 2-dimensional space, a circle and in 3-d, a sphere.

In 2-dimensional space, a circle. In 3-dimensional space, a sphere.

A circle or sphere or hypersphere in 2 or 3 or more dimensions (respectively).

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The set of all points in space that are the same distance from a given point is called a sphere.

A spherical surface, with its center at the given point, and its radius equal to the given distance.

The set of all points a given distance from a center point is a circle. The given distance is the radius, and the given point is the center. Or, in 3 dimensional space, a sphere.

In three dimensions, the solid defined as being bound by the set of points at a given distance form a point is a sphere. In two dimensions, the figure defined as being bound by the set of points at a given distance from a point is a circle. In one dimension, a line segment is bound by the two points at a given distance from a point.

The set of all points a given distance from a center point is a circle. The given distance is the radius, and the given point is the center. In 3 dimensional space, the set would be the surface of a sphere.

A circle, sphere or hyper-sphere - depending on the dimensionality of the space.

surface area of a cylinder? No. In 2-dimensional space, a circle and in 3-d, a sphere.

In 2-dimensional space, a circle. In 3-dimensional space, a sphere.

A circle or sphere or hypersphere in 2 or 3 or more dimensions (respectively).

That's a sphere whose radius is the constant equal distance.

By definition, a set of all points all the same distance from a given point is a circle (in two-dimensional space). To why take a pencil (or a math compass), place it on a sheet of paper and hold the eraser down on a single point. Without moving the eraser, move the pencil around. The length of the pencil does not change so you are drawing all the points that are the same distance from a given point. What shape does it make? A circle. FYI If you are dealing with 3-dimensional space, the answer is a sphere.

A globular sphere has all points at the same distance from an interiocenter point.