Which of the following is defined as a three-dimensional shape where all points on the surface are equidistant from the center?

The correct choice is a sphere, which is defined as a three-dimensional shape where all points on the surface are equidistant from the center. This means that if you were to draw lines from the center of the sphere to any point on its surface, those lines would all be the same length, demonstrating the uniformity of distance in a sphere.

In the context of geospatial science, a sphere is often utilized in mathematical and physical models, such as when attempting to represent the Earth in a simplified manner. Although the Earth is not a perfect sphere due to its rotation and various topographical features, the concept of a sphere serves as a fundamental basis for understanding three-dimensional shapes with constant radius.

The other options represent different types of shapes or models closely related to the Earth's surface. The geoid, for instance, is a model of Earth's shape based on mean sea level and gravitational variations but is more complex in nature. A reference ellipsoid is a mathematically defined surface that approximates the geoid; it accounts for the flattening at the poles and the bulging at the equator. An oblate ellipsoid is a specific type of reference ellipsoid that describes a shape flattened at the poles, which is closer to the Earth's actual shape than