We add up these volumes to get the total volume of our box.

Input := 


v[a_,b_] = (8-2a)(10-2a)Sqrt[a^2 - b^2] + 

				2  (8-2a) b Sqrt[a^2 - b^2]/2 +

				2  (10-2a) b Sqrt[a^2 - b^2]/2 +

				4 1/3 b^2 Sqrt[a^2 - b^2];