Question

Find the parametric representation for the surface:
The part of the sphere x^2 + y^2 +z^2 = 4 that lies above the cone z= sqrt(x^2 + y^2).

Answer 1

You can use spherical coordinates.

Answer 2

\[x=2\sin\phi \cos\theta\]
\[y=2\sin\phi\sin\theta\]
\[z=2\cos\phi\]
\[0\le \phi\le \pi \text{ and } 0\le \theta \le \pi\]

Answer 3

Mr. Math, I have to ask, would you not use:
\[x=2\sin(\phi)\cos(\theta); y=2\sin(\phi)\sin(\theta); z=2\cos(\phi); 0 \le \phi \le \frac{\pi}{4}; 0 \le \theta \le 2 \pi\]
Because the cone creates a 45 degree angle in the first quadrant of the x-y plane. So the phi angle (defined from the positive x-axis would only go down TO THE CONE, not the entire pi which would give you the whole sphere. It says above the cone, so would it be to pi/4?