1998 Gauss 8 Problem 22

A cube measures 10\,\text{cm}\times10\,\text{cm}\times10\,\text{cm}. Three cuts are made parallel to the faces of the cube as shown creating eight separate solids which are then separated. What is the increase in the total surface area?

\textbf{(A)}\ 300\,\text{cm}^2\quad \textbf{(B)}\ 800\,\text{cm}^2\quad \textbf{(C)}\ 1200\,\text{cm}^2\quad \textbf{(D)}\ 600\,\text{cm}^2\quad \textbf{(E)}\ 0\,\text{cm}^2

If there are no answer choices shown, enter a numerical answer.

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.