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A cylindrical can has a 1-inch radius and a height of 5 inches. If the cans must be stored in an upright position, what is the maximum number of cans that will fit on a shelf that is 4 feet long, 4 feet wide and 15 inches high?

 

Assume that the cylinders are packed according to a hexagonal packing.

 

 Dec 22, 2023
 #1
avatar+126665 
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4 feet  =  48  inches = width

 

Each can has a diameter=  2 in

 

So

 

48/2 =   24 cans can  be  packed in one row

And 23  can be packed in the next row

 

15 in / 5 =    3  =  number of  cans in a  stack

 

Each two rows   of cans occupy   [10 + 5sqrt (3)] in  of the length

 

So     integer ( 24  / [ 10 + 5sqrt 3 ]  )  =     1  two row unit

 

This means only  two rows of cans can  be fitted  lengthwise   

 

Total number of cans  =  3 ( 24 + 23)  =  147

 

cool cool cool

 Dec 22, 2023

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