Starting with a sphere, the goal is to cut it down to an “apple slice” or half hemisphere shape. The following was done to get the sphere to the hollow “apple slice” shape:

• With the sphere selected, go into Edit Mode (or press [Tab])
• Then hit the [B] key
• Hold down and drag to select the vertices/faces of interest
• Press the [Space] bar
• Type “delete” in the text field and press the [Return] key
• Select “vertices” or “faces” depending on how you are trying to go about it

That should do it. This is what I got after that workflow:

I then repeated the above workflow to get to a half hemisphere or “apple slice” shape. Next, the now hollow apple slice needed to be made solid. That was accomplished using the following workflow:

• Switch to Quad View by clicking “View” on the bottom left menu bar, then selecting “Quad View”
• Switch to Edit Mode just like in the previous workflow
• Press the [B] key, then hold down on the mouse and drag to select just a small piece of the edge of interest.
• On the bottom left menu bar, choose “Select”, then “Edge Ring”
• Press the [F] key

I did this workflow twice for each “wall” I needed to get the “apple slice” to be solid:

Done.

About my setup:

Blender 2.77 on OS X El Capitan 10.11.6, using MacBook Pro Mid-2009 13-inch Core2-Duo 2.26 GHz hardware.