Confined Volume Calculation: How to Determine the Volume Within a Given Surface?

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Homework Help Overview

The problem involves calculating the volume confined within a specific surface defined by a complex equation involving variables x, y, and z. The context suggests a focus on geometric interpretation and transformation of coordinates.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants discuss the potential for transforming the given equation into a simpler form, such as a sphere, by choosing appropriate coordinates. There is also inquiry into the necessary Jacobian for the transformation to spherical coordinates.

Discussion Status

The discussion includes attempts to identify suitable coordinate transformations and the implications of those choices. One participant expresses gratitude for a hint received, indicating some productive guidance has been shared.

Contextual Notes

There is mention of needing to use different variables and transformations, as well as concerns about the Jacobian, which suggests a level of complexity in the problem setup that may require further clarification or exploration.

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Homework Statement


calculate the volume confined within this surface
<br /> \left( x+y+z \right) ^{2}+ \left( 2\,x+y+z \right) ^{2}+ \left( 3\,x+<br /> 4\,y+z \right) ^{2}=4<br />

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The Attempt at a Solution


i know that i need to use different variables but i just can't make it
 
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What choice of coordinates will turn that into a sphere u^2+v^2+w^2=4??
 
Dick said:
What choice of coordinates will turn that into a sphere u^2+v^2+w^2=4??

even if i do choose
u=x+y+z
v=2x+y+z
w=3x+4y+z

which jacobian will i use?
because i need to use another transformation to spheerical coord...
 
Last edited:
never mind got iy thanks allot for the hint
 

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