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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?

Guest Oct 11, 2014

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 #2
avatar+17711 
+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
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3+0 Answers

 #1
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4×4×4=64 cc

Guest Oct 11, 2014
 #2
avatar+17711 
+10
Best Answer

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
avatar+91469 
0

I like your logic Geno 

Melody  Oct 12, 2014

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