hello,

i'm having little problem with this .... i need to find volume of figure

$\displaystyle (x-1)^2 +y^2 +z^2 = 1 $

$\displaystyle y\ge 0 $

using spherical coordinates ...

now i realize that this is just a sphere, actually half of the sphere with center in (1,0,0) and radius of 1 ... that is not the problem... and it's volume should be as half of volume of same sphere in center (0,0,0) ...

but i'm having problem how to figure out limits for variables ...

i know that

$\displaystyle x = r \cdot \cos {\theta} \cdot \sin {\varphi} $

$\displaystyle y = r \cdot \sin {\theta} \cdot \sin {\varphi} $

$\displaystyle z = r \cdot \cos {\theta} $

$\displaystyle J = r^2 \sin {\varphi} $

but how does them look like that if figure is shifted from (0,0,0) ? or is it something like :

if shifted

$\displaystyle (x-1)^2 +(y+1)^2 +(z-1 )^2 = 1 $

i need to use something like

$\displaystyle x = r \cdot \cos {\theta} \cdot \sin {\varphi} +p $

$\displaystyle y = r \cdot \sin {\theta} \cdot \sin {\varphi} -q$

$\displaystyle z = r \cdot \cos {\varphi} + t $

and J should be the same ? ? ? ?

any help will be very much appreciated