Answer
$x =4 \sin v \cos u; y=4 \sin v \sin u$ and $z=4 \cos v$; $0 \lt u \lt 2\pi$ and $\dfrac{\pi}{4} \lt v \lt \dfrac{\pi}{2}$
Work Step by Step
We are given the equation of a sphere as: $x^2+y^2+z^2=16 $
and $2\sqrt 2 \lt z \lt 4$
The parametric description of a sphere with radius $a$ can be expressed as:
$x =4 \sin \phi \cos \theta; y=4 \sin \phi \sin \theta$ and $z=4 \cos \phi$
Suppose that $u=\theta$ and $v=\phi$
Thus, the parametric form of a sphere can be expressed as:
$x =4 \sin v \cos u; y=4 \sin v \sin u$ and $z=4 \cos v$; $0 \lt u \lt 2\pi$ and $\dfrac{\pi}{4} \lt v \lt \dfrac{\pi}{2}$
