SOLUTION: You have a box that measures 2.6 ft, 2.8 ft by 3.0 ft on each interior edge, how many smaller boxes that measure 5.0 inch on each exterior edge can you fit into the larger box?

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Question 1067693: You have a box that measures 2.6 ft, 2.8 ft by 3.0 ft on each interior edge, how many smaller boxes that measure 5.0 inch on each exterior edge can you fit into the larger box?
Here is what I have tried:
2.6 ft (converted to)----> 31.2 in./5 = 6.24 in
2.8 ft (converted to)----> 33.6 in./5 = 6.72 in
3.0 ft (converted to)----> 36 in./5 = 7.2 in
6.24 in x 6.72 in x 7.2 in = 301.9161 (and you can fit .9161 of a box in, so my final answer came out to be 301) FINAL = 301 Boxes
My teacher's answer key said the answer is 252 but I don't agree.
Answer by KMST(5397) (Show Source):
You can put this solution on YOUR website!
Your teacher's point is that
along the 2.6 ft edge you could fit 6 boxes,
along the 2.8 ft edge you could fit 6 boxes, and
along the 3.0 ft edge you could fit 7 boxes.
That is boxes,
one bottom layer with 6 rows of 6 boxes each,
and 6 more layers like that on top.
A layer of 6 rows of 6 small boxes each covers
a by 30 inch square
on the 31.2 inch by 33.6 inch bottom of the large box.
There will be some wasted space that you can fill with bubble wrap,
but you cannot fit more boxes on those narrow gaps.
After piling 7 layers like that,
the small boxes will reach a height of
,
and that is 1 inch below the top of the box,
but you cannot fit 5-inch boxes in a 1-inch space,
so you will need to fill that wasted space with packing material.
Only of the
of available space
are filled with the small boxes.
The rest is wasted space filled with packing material.