# Parametric Equation of a sphere

1. Jan 15, 2010

### anubis01

1. The problem statement, all variables and given/known data
Find parametric equations for the part of sphere x2+y2+z2=9 that lies between the planes y=1 and y=2.

2. Relevant equations

3. The attempt at a solution

Okay knowing that the p=3 I wrote the parametric equations for a sphere as
x=3sin$$\phi$$cos$$\theta$$ y=3sin$$\phi$$sin$$\theta$$
z=3cos$$\phi$$ now the phi bound is 0<$$\phi$$<$$\pi$$
but I'm not sure what to write for the $$\theta$$ bound.

2. Jan 15, 2010

### Dick

It would be easier if they said between z=2 and z=1, right? Then you would just have to restrict phi. There's no reason why you can't interchange say, y and z in your parametrization.

3. Jan 15, 2010

### anubis01

Oh okay so I can say z=3cos$$\phi$$
and from there plug in the values to find the $$\phi$$ bound to be cos(1/3)-1<$$\phi$$<cos(2/3)-1 and the $$\theta$$ bound should just be 0< $$\theta$$<2$$\pi$$

4. Jan 15, 2010

### Dick

Right. But they did say y=1 and y=2. You'll also have to tweak your parametrization so y=3*cos(theta) instead of z=3*cos(theta).

5. Jan 15, 2010

### anubis01

oh so then phi bound should be 0<$$\phi$$<$$\pi$$ and since y=3cos$$\theta$$ the bounds for $$\theta$$ are
cos(1/3)-1<$$\theta$$<cos(2/3)-1

6. Jan 15, 2010

### Dick

Sorry, sorry!!! I meant to say your parametrization has z=3*cos(phi) and you want to change it so that y=3*cos(phi). Leave theta as it is.

7. Jan 15, 2010

### anubis01

alright i think i got it now. So bound for theta 0<$$\theta$$<2$$\pi$$
y=3cos$$\phi$$ the bounds for phi are then
cos(1/3)-1<$$\phi$$<cos(2/3)-1

and the parametric equation for x=3sin$$\phi$$cos$$\theta$$
and z=3sin$$\phi$$sin$$\theta$$

8. Jan 15, 2010

### Dick

That looks good to me.

9. Jan 15, 2010

### anubis01

alright thank you for all the help, its much appreciated.