What is the volume?

This is the first time that you've made a mistake!!!

The height for the original part is  10 cm

Never mind that the solid is standing at the angle of 60 degrees.

If you cut the bottom of the solid at the angle of 30 degrees, and put that part on the top of the solid, 

the height is going to be exactly 10 cm.

So, we have...      V = (10 * 4 * 3) / 8 

                      or     V = 5 * 2 * 1.5  

Imagine the angle was 89° (or even 90°). Do you think the volume would still be the same?

(Incidentally, I make mistakes all the time!  That's why it's incumbent on all posters to check the answers themselves.)

I think I made a huge mistake. I've just realized that the dimension 4 is given at a certain angle. 

corrections:        V = 5 * 1.5 * sqrt(3)               V = [10 * 3 * 2sqrt(3)] / 8  

I apologize, Alan!!!  Your answer is, of course, correct!!! 

No problem!