# Ugly volume caculation

1. Aug 20, 2008

### supercali

1. The problem statement, all variables and given/known data
calculate the volume confined within this surface
$$\left( x+y+z \right) ^{2}+ \left( 2\,x+y+z \right) ^{2}+ \left( 3\,x+ 4\,y+z \right) ^{2}=4$$

2. Relevant equations

3. The attempt at a solution
i know that i need to use different variables but i just cant make it

2. Aug 20, 2008

### Dick

What choice of coordinates will turn that into a sphere u^2+v^2+w^2=4??

3. Aug 20, 2008

### supercali

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: Aug 20, 2008
4. Aug 20, 2008

### supercali

never mind got iy thanks allot for the hint