3. three-dimensional figure with all of its points equidistant from a center

The three-dimensional figure you are describing is a sphere. ### Explanation: 1. **Definition of a Sphere**: A sphere is defined as the set of all points in three-dimensional space that are at a constant distance (radius) from a fixed point (the center). 2. **Properties**: - **Center**: The fixed point from which all points on the sphere are equidistant. - **Radius**: The distance from the center to any point on the surface of the sphere. - **Surface Area**: The surface area \( A \) of a sphere can be calculated using the formula: \[ A = 4\pi r^2 \] - **Volume**: The volume \( V \) of a sphere can be calculated using the formula: \[ V = \frac{4}{3}\pi r^3 \] ### Conclusion: In summary, a sphere is a three-dimensional figure characterized by all points being equidistant from a central point, with specific formulas for its surface area and volume based on its radius.