8. A juice manufacturer wants to sell juice packs of
180 mL. He can choose any one of the following
a carton of 5cm by 6cm by 6cm; 3 cm by 5cm by
12 cm; or 4cm by 5cm by 9cm. The cost of the
carton is directly proportional to the surface area of
paper board sheet used in making them. Which one
should he choose and why?
Answers
a carton of 5cm by 6cm by 6cm will be chosen as it has least surface area hence least cost
Step-by-step explanation:
a carton of 5cm by 6cm by 6cm
Volume = 5 * 6 * 6 = 180 cm³
Surface area = 2( 5 *6 + 6 * 6 + 5*6) = 192 cm²
3 cm by 5cm by 12 cm
Volume = 3 * 5 * 12 = 180 cm³
Surface area = 2( 3 *5 + 5 * 12 + 3*12) = 222 cm²
4cm by 5cm by 9cm
Volume = 4 * 5 * 9 = 180 cm³
Surface area = 2( 4 *5 + 5 * 9 + 4*9) = 202 cm²
The cost of the carton is directly proportional to the surface area of paper board sheet used in making them
Hence Surface area should be minimum for a given volume to reduce cost
Volume of all is same
Surface area 192 cm² is minimum of carton of 5cm by 6cm by 6cm
so a carton of 5cm by 6cm by 6cm
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