Which of the following is a parametric representation of the given surface? [Assume the axes are oriented as shown in the figure below.]

Question

Which of the following is a parametric representation of the given surface?  [Assume the axes are oriented as shown in the figure below.]

Quizplus · Accepted Answer

The surface shown in the figure is a part of a sphere with radius 2 centered at the origin. A parametric representation of this sphere can be given as follows:
x = 2sinφcosθ
y = 2sinφsinθ
z = 2cosφ
where 0 ≤ φ ≤ π and 0 ≤ θ ≤ 2π.
The parametric representation in choice C matches this equation, so it is the correct choice. The other choices do not match this equation and therefore cannot be correct.

Which of the Following Is a Parametric Representation of the Given