Question

Find a parametric representation for the surface. The part of the sphere x2 + y2 + z2 = 16 that lies between the planes z = −2 and z = 2. (Enter your answer as a comma-separated list of equations. Let x, y, and z be in terms of θ and/or ϕ.)

Answer 1

The standard choice would be the usual representation in spherical coordinates. Let

$x=4\cos\theta\sin\varphi$

$y=4\sin\theta\sin\varphi$

$z=4\cos\varphi$

We get the part of the sphere between the planes $|z|=2$ with $0\le\theta\le2\pi$ and $\dfrac\pi3\le\varphi\le\dfrac{2\pi}3$.