Solving for Volume in a Complex Figure: Ostrogradsky and Spherical Coordinates

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Homework Help Overview

The discussion revolves around finding the volume of a complex figure defined by the equation (x^2+y^2+z^2+1)^2=8*(x^2+y^2), involving concepts from calculus and coordinate transformations, specifically Ostrogradsky's theorem and spherical coordinates.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to apply Ostrogradsky's theorem and spherical coordinates but struggles with determining the boundaries of the volume. Some participants question the understanding of the theorem and suggest considering the symmetry of the figure.

Discussion Status

Participants are engaged in clarifying the problem and exploring different approaches. A hint regarding the cylindrical symmetry of the figure has been provided, which may guide the original poster towards a potential path forward.

Contextual Notes

There is a mention of the need for the original poster to share their previous attempts, which aligns with the forum's policy for collaborative help. The discussion also reflects some uncertainty regarding the application of specific mathematical concepts.

DianaSagita
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Volume Integral! Help!

I need help with this:

Find volume of figure bounded with surface (x^2+y^2+z^2+1)^2=8*(x^2+y^2)

I tried Ostrogradsky, and spherical coordinate system with it, but I can't find boundaries...

PLEASE! HELP ME!
 
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Please show us what you tried, then we'll help you. That's the policy here.
 
Welcome to PF!

DianaSagita said:
I need help with this:

Find volume of figure bounded with surface (x^2+y^2+z^2+1)^2=8*(x^2+y^2)

I tried Ostrogradsky, and spherical coordinate system with it, but I can't find boundaries...

PLEASE! HELP ME!

Hi DianaSagita ! Welcome to PF! :smile:

(what's Ostrogradsky? :confused: )

(oh, have a squared: ²)

Hint: it's obviously cylindrically symmetric, so write x² + y² = r², to give:

(r² + z² + 1)² - 8r² = 0. :smile:
 
Thanks a lot. I did it! :)
 

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