You are a manufacturer of boxes used for take out Chinese food. A supplier comes
ID: 18500 • Letter: Y
Question
You are a manufacturer of boxes used for take out Chinese food. A supplier comes to you and asks you for help in solving his problems. When people order food in the family size, the food gets to the customers home while it is still warm. But, when they order food in individual sized portions the food is always cold when they get home. Being the scientists that you are, you go to the restraint and order the individual serving of almond chicken and a family sized serving. Sure enough, by the time you get home the individual serving is cold, while the family sized is still piping hot. The family sized order comes in a box which is 3 decimeters each side, while the individual serving comes in a box which is 2 decimeters on a side. A square decimeter of cardboard used in making the boxes costs $ 0.01. (one cent)Using the information given please answer each of the following questions: NO WORK NO CREDIT! PLEASE SHOW YOUR WORK!!
A. Why are the individual servings cooling so much faster?
B. How much more chicken can be held in the family size box (cubic decimeters is fine for your units.)
C. How much does it cost you for the cardboard to make 2 family sized boxes?
D. How much does it cost you for the cardboard to make 7 individual serving boxes?
E. How much chicken will be held in the 2 family sized boxes?
F. How much chicken will be held in the 7 individual sized boxes?
Explanation / Answer
A. Heat transfer depends on the total surface area per unit volume. surface area of a box=6xd^2 volume of a box=d^3 so surface area per unit volume=6d^2/s^3=6/d which is 3 for individual serving and 2 for family serving. As the total surface area per unit volume is more in case of individual servings than in case of family servings the individual serving are cooling faster. B.Volume of chicken in individual servings=d^3=2^3=8 Volume of chicken in family servings=d^3=3^3=27 So 27-8=19 cubic decimeters of more chicken can be held in the family size box C.Surface area of a family sized box=6d^2=6x3^2=54 So total surface area of cardboard used in 2 family sized boxes=2x54=108 Thus total cost of cardboard=108x0.01=$1.08 D.Surface area of 7 individual serving box=7x6d^2=7x6x2^2=168 Thus total cost of cardboard=168x0.01=$1.68 E.Amount of chicken in 2 family sized boxes=2xd^3=2x3^3=54 cubic decimeters F. Amount of chicken in 7 individual serving boxes=7xd^3=7x2^3=56 cubic decimeters
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