Jerry is packing cylindrical cans with diameter 6 in. and height 10 in. tightly into a box that measures 3 ft by 2 ft by 1 ft. All rows must contain the same number of cans. The cans can touch each other. He then fills all the empty space in the box with packing foam. How many cans can Jerry pack in one box? Find the volume of packing foam he uses. What percentage of the box's volume is filled by the foam?

Answer 1

so each box has just 1 level of cans since height = 1ft

3ft x 2ft = 36in x 24 in
so whe have 36/6 = 6 cans in one dimension
and 24/6 = 4 cans in the other dimension
we have 6x4 = 24 cans per box ==> answer 1
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volume of the box = 36x24x12 = 10368 in^3
volume of 1 can = Pi*3²*10 = 3.1416*90 = 282.744
volume of 24 cans = 24*282.744 = 6785.856
volume of the foam = 10368-6785.856 = 3582 in^3 ==>answer 2
percentage of the box's volume is filled by the foam
= 3582/10368 = 34.6%