Stacie builds a cube using 343 blocks of wood. She decides to paint the cube green. How many of the wooden blocks will have at least one side painted green?
A) 105
B) 218
C) 125
D) 238
E) 245
IMAT 2024 · Question 8
Q8 - Problem solving
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The correct answer is B) 218.
343 = 7³, so it's a 7 × 7 × 7 cube.
The blocks with no paint are the ones completely hidden inside. Remove one layer from each face and you're left with a 5 × 5 × 5 cube, which is 125 blocks.
343 − 125 = 218 painted blocks.
125 is in the options too, as the count of the unpainted ones.
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