I have a solid cube with its dimensions 2 units in length. I have drill-bit of radius 1 unit.

I drill a hole through the centre of each face through to the other side.

When I have finished I am left with 8 identicle corner shapes.

I would like to see the all working for the calculation of the volume of one of these corner bits?

The actual volume was provided in part 1 of the question, see :

http://www.experts-exchange.com/Miscellaneous/Math_Science/Q_21095902.html
I would now like to see how the formula was arrived at.