A vineyard is designing a new cylindrical barrel with a lid in which to age wine. They are planning to create a container with a volume of 450 000 cm3 that is as cost efficient as possible. a) Determine the dimensions of the barrel that requires the least material. Round the dimensions to the nearest hundredth of a centimetre. 2 b) If oak costs $0.005/cm , find the cost to make 100 oak barrels.
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Many wines improve in quality during barrel and bottle storage. Such wines eventually reach their peak and with further aging begin to decline. During the aging period, acidity decreases, additional clarification and stabilization occur as undesirable substances are precipitated, and the various components of the wine form complex compounds affecting flavour and aroma.
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