Problem 25 (2009 AMC 8)

A one-cubic-foot cube is cut into four pieces by three cuts parallel to the top face of the cube. The first cut is $\frac{1}{2}$ foot from the top face. The second cut is $\frac{1}{3}$ foot below the first cut, and the third cut is $\frac{1}{17}$ foot below the second cut. From the top to the bottom the pieces are labeled $A$, $B$, $C$, and $D$. The pieces are then glued together end to end as shown in the second diagram. What is the total surface area of this solid in square feet? [See figure in original PDF]