Need help setting up a math problem

[TecHNooB]

How would I find a parametric representation for the following surface:

A sphere x^2 + y^2 + z^2 = 16, lies between z = -2 and z = 2.

 

[TecHNooB]

Ok, shot in the dark.

I set z = SQRT(16 - x^2 - y^2)
x = r cos(theta)
y = r sin(theta)

Since the sphere is between z = 2, z = -2, x^2 + y^2 = 12 so r^2 = 12. So I paramatized the surface in terms of r and theta. So...

z = SQRT(16 - r^2)
x = r cos(theta)
y = r sin(theta)

0 <= r <= 2*SQRT(3)
0 <= theta <= 2*pi

Is this remotely correct? Where are all the ATOT smarties? 🙁

 

[DrPizza]

Here are two pretty good sources that'll help you. It pretty much becomes a matter of just plugging in the numbers, but these sites also provide a bit of an explanation. (I just got done explaining synthetic division in another thread... some of these replies simply take too long.)

mathworld.wolfram.com
(the makers of mathematica are always an excellent source 🙂 )

And, of course, Ask Dr Math:
DrMath here

 

[txrandom]

z = rsin(phi)
y = rcos(phi)sin(theta)
x = rcos(phi)cos(theta)

 

[TecHNooB]

I know how to paramatize a sphere. But this one had its hair and balls shaved. It's not even a sphere anymore 🙁