Problem 314

The original prism has four faces that are 4 by 2 rectangles, and two faces that are 2 by 2 rectangles. Thus, the surface area of the original prism is $4(4 \cdot 2)+2(2 \cdot 2)=32+8=40$. When a 1 by 1 by cube is cut out, a 1 by 1 square is removed from each of three faces of the prism, but three new 1 by 1 squares become part of the surface area. In other words, there is no change to the total surface area. Therefore, the surface area of the new solid is also 40.