A solid 5x5x5 cube is composed of unit cubes. Each face of the large, solid cube is partially painted with gray paint, as shown.

What fraction of the entire solid cube's unit cubes have no paint on them? Express your answer as a common fraction.

Guest Nov 25, 2019

#1**+1 **

I think the easiest way would be to count the cubes that do have paint on them and then subtract.

Each of the 8 vertices has paint on three sides of one cube* = 8 cubes

Each of the 6 faces has paint on one side of eight "center" cubes = 48 cubes

Total cubes with paint are 56 subtracted from 125 cubes in the block = 69 cubes with no paint

The fraction of cubes with no paint is 69 / 125

* Although each corner cube has paint on three sides, it's still just one cube.

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Guest Nov 26, 2019

#1**+1 **

Best Answer

I think the easiest way would be to count the cubes that do have paint on them and then subtract.

Each of the 8 vertices has paint on three sides of one cube* = 8 cubes

Each of the 6 faces has paint on one side of eight "center" cubes = 48 cubes

Total cubes with paint are 56 subtracted from 125 cubes in the block = 69 cubes with no paint

The fraction of cubes with no paint is 69 / 125

* Although each corner cube has paint on three sides, it's still just one cube.

_{.}

Guest Nov 26, 2019