This reminds me of the 3b1b about average shadow.
Similar question is average depth of a cube in that direction . Volume = Depth * Shadow
D = V / S = V / (A/4) = 8 / (24 / 4) = 4/3
A point in the cube, on average is closer than 4/6 to a face, half of the depth. the answer is therefore ≤ 4/6
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