SOLUTION: We glued together several unit cubes to make a solid (no hole in the middle) big cube. There are a total of 80 unit cubes that are either at the vertices or on the edges of the

Algebra ->  Volume -> SOLUTION: We glued together several unit cubes to make a solid (no hole in the middle) big cube. There are a total of 80 unit cubes that are either at the vertices or on the edges of the      Log On


   



Question 808851: We glued together several unit cubes to make a solid (no hole in the
middle) big cube. There are a total of 80 unit cubes that are either at the
vertices or on the edges of the big cube. How many unit cubes did we use
to build the big cube?

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If I say that +x+ is the number of cubes
along an edge including the corners, then
+x+-+2+ is the number not including
the corners.
Going around the cube I have +12+
edges and +8+ corners, so
+12%2A%28+x+-+2+%29+%2B+8+=+80+
+12x+-+24+%2B+8+=+80+
+12x+=+80+%2B+16+
+12x+=+96+
+x+=+8+
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The number of unit cubes should be
+8%5E3+=+512+
512 unit cubes