I would like to know how to graph a surface area in spherical given the value of the area. It is because I would to calculate the surface area and I dont know how to visualize which side of the sphere it is. So I can use the correct differential surface area equation.
Here is an example,
Calculate the surface area using differential surface area dS.
$r = 10$, $\pi/4 < \theta < 2\pi/3$, $0 < \phi < 2\pi$
You can get Wolfram alpha to generate your graph if you can parametrize your surface as $$x=f(u,v),y=g(u,v),z=h(u,v)$$ using ParametricPLot$3$D. Using the standard parametrization in your example WA generates the following graph
Area of this surface is $$\mathrm{\int_0^{2\pi}\int_{\pi/4}^{2\pi/3}10^2\sin\theta d\theta d\phi}=100\pi(\sqrt{2}+1)$$