Here is a visual representation of the equation \( z^2 = r^2 + 4 \), which resembles a hyperboloid of one sheet. This plot highlights the symmetrical curvature of the surface, where the constant term "4" shifts the shape vertically in the \( z \)-axis.

Would you like further details on this equation or the drawing?

Here are five related questions to consider:
1. How does changing the constant "4" in the equation affect the shape of the hyperboloid?
2. What is the general form of a hyperboloid of one sheet?
3. Can this equation represent a physical object or system?
4. How would the surface change if \( z^2 = r^2 - 4 \) instead?
5. How do hyperboloids relate to hyperbolic geometry?

**Tip:** In 3D geometry, adding a constant to a quadratic equation often translates the graph along the corresponding axis without altering its fundamental shape.

Explore the 3D graph of the equation z^2 = r^2 + 4, which represents a hyperboloid of one sheet. This page provides insights into its structure, effects of the constant term on the surface, and relevant theorems in geometry. Suitable for advanced high school students studying 3D shapes.

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