Question 724386: Labels for a soup can are cut from a sheet of paper that is 2x3ft. The soup can has a circumference of 8in and a height of 6in. What is the maximum number of labels that can be cut from the sheet of paper?
Please answer because I asked this question earlier and nobody helped.
THANKS
Answer by KMST(5328)   (Show Source):
You can put this solution on YOUR website! The label will be a rectangle.
Its width/height will be the height of the can.
Its length must be at least the circumference of the can. A little extra length so the ends overlap a bit and can be glued together would be nice. The soup cans are usually labeled like that. However if we just glue the ends to the can, without overlapping we can save some paper and get more labels.
MY APPROACH:
A 6 inch wide strip cut along the 2-foot length of the paper would be 6 inches wide by 24inches (2 feet) long. From there we can cut 3 labels because 3x8inches=24inches.
More strips could be cut in the same way, and as two strips would take 2x6inches=12inches=1foot, we can get 2x3strips=6strips from the 3-foot long piece of paper.
As we get 3 labels per strip, the total number of labels is 6x3=18 labels from one sheet of paper.
Here is my drawing of the piece of paper with the cut lines marked  The numbers are the measurements in inches.
THE OTHER APPROACH
The sheet of paper measures 24 inches by 36 inches, because 1 foot is 12 inches and
2feet x 12inches/foot = 24 inches
3feet x 12inches/foot = 36 inches
The total suface area of the sheet, in square inches is
(24 inches) x (36 inches) = 864 square inches
The total surface area of one label is
(8 inches) x (6 inches) = 48 square inches
We can find the numbers of labels we can get per sheet by dividing the 864 square inches of space available by the 48 square inches required by each label.
NOTE: I do not like the second approach, but your teacher may love it.
I don't like it because:
It loose sight of reality, and instead fixates in robot-like calculations with big numbers.
In some cases, the total surface area avaiulable divided by the are required for one label gives an unrealistic number of labels, since they will not fit without wasted space, and would require that you glue together little cutout p[ieces to make some patchwork labels.
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