Question 9

To divide a cube into $8$ smaller cubes of equal size ($\frac{1}{2} \times \frac{1}{2} \times \frac{1}{2}$ of the original dimensions), we make one straight planar cut bisecting each of the three mutually perpendicular axes ($x, y, z$):

• Cut 1 (parallel to the $xy$-plane): divides the cube into $2$ equal halves.
• Cut 2 (parallel to the $yz$-plane): divides the $2$ halves into $4$ equal quarters.
• Cut 3 (parallel to the $xz$-plane): divides the $4$ quarters into $8$ equal octants.

Thus, the minimum number of cuts required is $3$.