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# A hollow cube was built using linking cubes

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A hollow cube was built using linking cubes that each had a volume of 1 cm2. There were 4 cubes on a side. What was the total volume of the cubes used?

Oct 11, 2014

#2
+17747
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I'm picturing something that looks like a Rubik's cube, but each side is  4 x 4.

The top side is  4 x 4             (so 16 cubes);

the bottom side is also 4 x 4  (so another 16 cubes)

the front side is  4 x 4  but  we already have cubes on the top and on the bottom,                                                                                       so all we need are another  8 cubes

same for the back side           (so another  8  cubes).

for the left side, we have its top row, its bottom row, its left column and its right column,

so all we need are  4  more cubes

same for the right side          (so another 4  cubes )

For a total of 56 cubes.

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Another way to look at this (perhaps easier) is to find the total number of cubes necessary if it were hollow:        4 x 4 x 4  =  64

And then subtract out the inside; which is a  2 x 2 x 2  cube  =  8

For a total of  64 - 8  =  56  cubes

Oct 11, 2014

#1
0

4×4×4=64 cc

Oct 11, 2014
#2
+17747
+10

I'm picturing something that looks like a Rubik's cube, but each side is  4 x 4.

The top side is  4 x 4             (so 16 cubes);

the bottom side is also 4 x 4  (so another 16 cubes)

the front side is  4 x 4  but  we already have cubes on the top and on the bottom,                                                                                       so all we need are another  8 cubes

same for the back side           (so another  8  cubes).

for the left side, we have its top row, its bottom row, its left column and its right column,

so all we need are  4  more cubes

same for the right side          (so another 4  cubes )

For a total of 56 cubes.

-------------------------------

Another way to look at this (perhaps easier) is to find the total number of cubes necessary if it were hollow:        4 x 4 x 4  =  64

And then subtract out the inside; which is a  2 x 2 x 2  cube  =  8

For a total of  64 - 8  =  56  cubes

geno3141 Oct 11, 2014
#3
+95334
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