Sophie has a box of trail mix that is a length of 10 1/2 inches and the width is 4 1/2 and the height is 8 inches. The box doesn't fit into Sophie's cupboard so she puts it into smaller boxes that will fit into her cupboard. Will 3 boxes with dimensions 6 1/4 inches by 3 1/4 inches by 6 inches fit in the cupboard?

Yes, because the 3 smaller boxes share a volume of 365 inches as opposed to 378 of the bug box

Step-by-step explanations:

If the big box couldn't fut into the cupboard that means that it has a volume with dimensions that are a bit too much since the volume talks about the capacity of any material to be able to occupy as much space as possible.

The big box had dimensions of 10½,4½ and 8 inches and the volume is derived by multiplying the height, width and the length.

V = 10½ * 4½ * 8

= 378 in³

And the dimensions of the smaller boxes are 6¼,3¼ and 6 inches.

Their volume will be:

V = 6¼ * 3¼ * 6

= 121⅞

And to find the volume of all 3 boxes, all we have to do is to multiply the volume that we have just gotten by 3

121⅞ * 3 = 365⅝.

From the above we can all agree that the smaller boxes share a smaller volume as opposed to the bigger box, but since we weren't told the specific volume that the cupboard will be able to accommodate, we will have to believe that anything smaller than 378 will be enough for the cupboard