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do you convert feet to inches first before calculating area?
Cans to store food are made from rectangular sheets of tin that measure 6 feet by 80 ft. A standard tin can measures about 4.5 inches tall and has a circumference of aobut 9.5 inches. Asuuming there is as 5% area added to each piece (2 lids and one lateral piece) for overlap to seal the can shut, how many complete cans can be made from one sheet of tin? EXTRA BONUS: how much tin is wasted?
3 Answers
- SueLv 79 years agoFavorite Answer
Since circumference is 9.5in then (C= π d) diameter is about 3 inches making the radius 1.5in
Area of each lid = π r² = 7.07 in² so two lids = 14.14in²
Lateral area = Circumference * height= 9.5*4.5= 42.75 in²
Each can 14.14 + 42.75 = 56.89 in²
56.89 * 1.05 = 59.73in² will be used for each can including the overlap allowance.
6 feet = 6*12= 72 in
80 feet= 80*12 = 960 in
Metal sheet Area = 72* 960 = 69,120 in²
69,120 /59.73 = 1157 whole cans wasting 12.39 in²
But this ignores the fact that each can will use a rectangular area of 9.5 (circumference straighted out) by 10.5 ( 4.5 + two 3in diameters, one at each end) then add 5% overlap in each direction you get a rectangle 9.975 by 11.025 for each can which gives you 109.97 in² per can
so 69,120 /109.97 = 628 whole cans wasting 58.84in²