how many 2" x 6" x 2" boxes would fit in a 10" x 20" x 10" box

Question

Have to find the maximum number possible

Answer 1

Hi Alexa,

 

If you draw a diagram, you will see that you can stack three of the smaller boxes inside the big box --> 6" x 3 = 18" which is less than the 20" height of the big box.

 

Across, you can fit 5 small boxes each way --> 5 x 2" = 10" which is the width and length of the big box.

 

So you have 25 boxes spread out on the bottom and then another two levels going up for a total of 3 x 25 = 75 boxes.

 

But then you can lie some boxes down across the top of your three levels since you have a 2 inch space up there.  You can fit 5 more small boxes lying down across one row.  Now there's a 4" x 10' space where can can fit another two small boxes lying the other way.  So 7 more boxes + 75 boxes = 82 boxes all together.

 

Dan