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

#2**+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.

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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

geno3141
Oct 11, 2014

#2**+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