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?
+23246 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
+23246 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
