A milk retailer wishes to design a milk carton with a square cross-section, as

Elementary Geometry For College Students, 7e
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Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
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Chapter9: Surfaces And Solids
Section9.1: Prisms, Area And Volume
Problem 40E: As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in....
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A milk retailer wishes to design a milk carton with a square cross-section, as
illustrated in Figure 1, containing two pints of milk (2 pints = 1.136 litres). The carton
is made from a rectangular sheet of waxed cardboard. It folds it into a square tube,
seals down the edge, and then folds and seals the top and bottom. To make the
resulting carton airtight and robust for handling, an overlap of at least 5mm is
needed. The procedure is illustrated in Figure 2. As the milk retailer will be using
many such cartons, there is a requirement to use the design that is least expensive
to produce. In particular, the retailer desires a design that minimizes the amount of
waxed cardboard used. Determine the dimensions of the container as per retailer
requirements.
5 mm overlap
Fresh Milk
2 pints
h
(1.136 liters)
5 mm overlap
50 тm <b < 100 тm
Figure 1: Milk container dimensions
Figure 2: Milk container overlaps
Transcribed Image Text:A milk retailer wishes to design a milk carton with a square cross-section, as illustrated in Figure 1, containing two pints of milk (2 pints = 1.136 litres). The carton is made from a rectangular sheet of waxed cardboard. It folds it into a square tube, seals down the edge, and then folds and seals the top and bottom. To make the resulting carton airtight and robust for handling, an overlap of at least 5mm is needed. The procedure is illustrated in Figure 2. As the milk retailer will be using many such cartons, there is a requirement to use the design that is least expensive to produce. In particular, the retailer desires a design that minimizes the amount of waxed cardboard used. Determine the dimensions of the container as per retailer requirements. 5 mm overlap Fresh Milk 2 pints h (1.136 liters) 5 mm overlap 50 тm <b < 100 тm Figure 1: Milk container dimensions Figure 2: Milk container overlaps
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