2024 Gauss 8 Problem 16

A block of wood in the shape of a rectangular prism has length 4 cm, width 4 cm, and height 7 cm. A cylindrical hole with radius 1 cm is drilled through the centre, as shown. To the nearest cm^3, what is the volume of the block of wood after the hole is drilled? (Note: The volume of a cylinder with radius r and height h is \pi r^2\ \text{h}.)

\textbf{(A)}\ 90 \text{ cm}^3\quad \textbf{(B)}\ 122 \text{ cm}^3\quad \textbf{(C)}\ 106 \text{ cm}^3\quad \textbf{(D)}\ 84 \text{ cm}^3\quad \textbf{(E)}\ 92 \text{ cm}^3

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