A cube is created by stacking 27 smaller cubes as shown
in the figure. A plane, going through vertices A, B and
C, cuts the cube as shown in the figure. How many
smaller cubes will get cut ?
in the figure. A plane, going through vertices A, B and
C, cuts the cube as shown in the figure. How many
smaller cubes will get cut ?
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Step-by-step explanation:
On the upper layer, it visibly cuts the 3 cubes from A to B. On the lower layer, it visibly cuts the 1 cube at C.
On the middle layer, it visibly cuts the 1 cube between A and C and similarly the not visible 1 cube between B and C.
This makes 6 "obvious" cuts.
There are 3 more cubes that get cut though, I've marked them here with the light blue smudge: image.
To see why, focus on the cube at A where I removed the solid line. Imagine that cube missing, then you'd be looking on the cube behind and the plane clearly cuts through the side of that cube (cut marked orange, the other visible edges of the cubes highlighted in dark blue).
For symmetry reasons the same happens for the 3 mentioned marked cubes, so we get a total of 9.