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The outside surface of a large cubical block is painted and then broken into unit cubes. If exactly 294 of the unit cubes were painted on just one side, what are the dimensions of the large cube?

 May 8, 2020
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The outside surface of a large cubical block is painted and then broken into unit cubes. If exactly 294 of the unit cubes were painted on just one side, what are the dimensions of the large cube? 

 

A cube has six sides so each side will be responsible for 294 / 6 = 49 of the painted cubes. 

 

You can't count the edges because they're painted on two sides except the corners which are painted on three sides. 

 

The 49 cubes on a side are in a square 7 x 7.  You didn't count the edges but they're still there, so each side is 9 x 9. 

 

The dimensions of the cube are 9 x 9 x 9 units

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 May 8, 2020

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