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The equation given is:

\[
x^2 + z^2 = 9
\]

This is the equation of a **circular cylinder**. It represents a cylinder with radius 3 (since \(9 = 3^2\)) oriented along the **y-axis** (as the variable \(y\) is absent from the equation, indicating no variation in that direction).

### Correct options:

1. **Surface Description:**
   The correct option is **D. circular cylinder**.

2. **Sketch the Surface:**
   Among the four 3D plots shown (A, B, C, and D), **D** is the plot of a circular cylinder, as it depicts a surface that wraps around an axis (likely the y-axis), matching the given equation \(x^2 + z^2 = 9\).

Would you like further explanation or details about cylindrical surfaces?

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Here are 5 follow-up questions to expand on this:

1. How does the absence of the \(y\) variable affect the shape of the surface?
2. What is the general form of a cylinder equation in 3D space?
3. Can the equation \(x^2 + z^2 = r^2\) represent any other geometric shape in different contexts?
4. How would the graph change if the equation included \(y^2\)?
5. What are the distinguishing features of an elliptic cylinder?

**Tip:** When identifying 3D surfaces, always check for missing variables, as they often indicate an extrusion along the corresponding axis!

Describe the surface given by the equation x^2 + z^2 = 9 and identify the correct sketch.

Explore how to identify and describe the surface represented by the equation x^2 + z^2 = 9. Learn why this equation forms a circular cylinder and how to correctly match the surface with its 3D graph. Ideal for undergraduate students studying analytic geometry.

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