+1248 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.
+129771 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
