MHB Surface Intersection: Paraboloid & Plane

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The intersection of the paraboloid defined by the equation x² + y² - z = 0 and the plane z = 2 results in a circle described by x² + y² = 2 at z = 2. This intersection is a curve, not a surface, and represents the boundary of a volume formed by the paraboloid and the plane. The area of the circular intersection is calculated as 2π, while the area of the surface of the paraboloid below this plane is found to be 26π/6. Both areas are derived using surface integral formulas, highlighting the relationship between the intersection and the bounded volume created by the two surfaces. Understanding these concepts is crucial for applying theorems like Gauss's divergence theorem in related problems.
  • #31
I like Serena said:
Yep. All correct. (Smile)

Erm... except for the $du=8dr$, which should be $du=8rdr$. :eek:
Apparently that is what you used anyway. (Mmm)

Yes,that's what I used.. (Nod)Thank you very much! (Mmm) (Smirk)
 

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