The equation \( x^2 + y^2 + z^2 = 4 \) represents a **sphere**.

- The general form of a sphere's equation is:
  \[
  (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2
  \]
  where \((h, k, l)\) is the center of the sphere, and \(r\) is the radius.

- In your equation \( x^2 + y^2 + z^2 = 4 \), the center is at the origin \((0, 0, 0)\), and the radius is \( r = \sqrt{4} = 2 \).

So, this describes a sphere with:
- **Center**: \((0, 0, 0)\)
- **Radius**: \(2\)

Would you like to explore more details about spheres?

Here are 5 related questions to deepen understanding:

1. How do you derive the equation of a sphere from geometric principles?
2. What happens if the equation of the sphere is \( (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2 \)?
3. How does a sphere differ from a circle in 2D geometry?
4. Can you graph this sphere in 3D space?
5. What is the surface area and volume of the sphere with radius 2?

**Tip:** The distance from any point on a sphere to its center is always the same—this is the radius.

𝑥^2 + 𝑦^2 + 𝑧^2 = 4 what shape is it?

Explore how the equation x^2 + y^2 + z^2 = 4 represents a sphere in 3D geometry. Learn about the sphere's center at (0, 0, 0) and radius 2, with detailed explanations of spherical geometry. This topic is ideal for students in Grades 9-12.

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