Definition of the region:

 reg := (
 r1^2 <= x^2 + y^2 + z^2 <= r2^2 && (* conditions on radius *)
 θ1 <= ArcTan[z, Sqrt[x^2 + y^2]] <= θ2 && (* conditions on polar angle *)
 φ1 <= ArcTan[x, y] <= φ2 (* conditions on azimuthal angle *)
 );

Definition of the parameters:

 {r1, r2, θ1, θ2, φ1, φ2} = {2, 2.2, 30°, 180°, 15°, 85°};

Plots:

 RegionPlot3D[ImplicitRegion[reg, {x, y, z}], 
 PlotPoints -> 80, Boxed -> False, ViewAngle -> 20°]

[![enter image description here][1]][1]

 RegionPlot3D[reg, {x, -2.5, 2.5}, {y, -2.5, 2.5}, {z, -2.5, 2.5}, 
 PlotPoints -> 80, Boxed -> False, ViewAngle -> 20°, Axes -> False, Mesh -> None]

[![enter image description here][2]][2]


 [1]: https://i.sstatic.net/r4leM.png
 [2]: https://i.sstatic.net/nKoYq.png