[Daniel Brim]

For a half sphere in Inventor, there are multiple ways to do it. On your sketch, you want to make a line (length doesn't matter as long as it intersects the arc that you are about to make). Then, make an arc with the radius that you want (ends up being the radius of the sphere). Make sure the center of the arc is coincident to the line.

There are several ways to go here:
1. Revolve the sketch you just made. I believe there is an option somewhere to tell it how far to go around and then enter 180 degrees. If this works, then great! You're done. If not, darn, but there is another way.
2. Revolve the sketch, and let it revolve all the way. Share the sketch that you made earlier, and make sure it is visible. Then click on extrude; make sure the area between the arc and the line is highlighted. Where it says distance, click the arrow and change it to all. Below that, there should be pictures of planes with arrows coming out of them. Click the one that has an arrow coming out of both sides. Make sure you are extruding away the piece, and click OK. Congrats, you're done!

HTH,
Daniel