FTCE Professional Education Practice Exam

Which space figure is characterized by having all points the same distance from its center?

1. A spheres

2. A cylinder

3. A pyramid

4. A tetrahedron

The correct answer is: A spheres

The space figure characterized by having all points the same distance from its center is a sphere. A sphere is defined mathematically as the set of all points in three-dimensional space that are a fixed distance (the radius) from a central point known as the center. This uniform distance from the center to any point on the surface of the sphere is what distinguishes it from other geometric figures. In contrast, a cylinder has two flat circular bases that are connected by a curved surface, but the distance from the center of the circular base to the outer surface changes based on the height. A pyramid has a base that is typically a polygon and triangular faces that converge to a single point, causing the distances from the center to vary based on the location on the base. Similarly, a tetrahedron is a three-dimensional shape with four triangular faces, and the distances to any point on the surface vary according to the position of those points relative to the vertices. Thus, the defining characteristic of a sphere is the consistent distance from the center to every point on its surface, making it the accurate answer to the question.