Final answer:
The equation z² = x² + y² represents a cone-like surface extending in both positive and negative z-directions.
Step-by-step explanation:
In three-dimensional space, the equation z² = x² + y² represents a cone-like surface. It is a double cone symmetrically extending in both positive and negative z-directions. The surface is formed by all the points (x, y, z) where the square of the z-coordinate is equal to the sum of the squares of the x and y coordinates.