Question

The ubiquitous 12oz aluminum cans used to distribute drinks in this country have a diameter of approximately 2.75 inches and a height of 5.0 inches. Estimate the amount of aluminum that could be saved if the cans were designed with the ratio d/h=1, while having the same volume as the standard 12oz can. A can manufacturer located in Oklahoma City produces aluminum cans for one major cola company. The distribution area for these cans includes about 13% of the US population located in New Mexico, Texas, Oklahoma, Kansas, Arkansas, Louisiana and southwestern Missouri. Inside the plant, there are eight stamping presses that manufacture can lids. Each press stamps two lids per stroke and on average runs at 500 strokes per minute. The machines run 24 hours a day for an average of 300 days per year. (The only time that the machines stop running is for two two week maintenance breaks, 10 holidays, and an additional 27 days due to miscellaneous break downs.) If the total volume of aluminum for one can is Vc=8.69×10−7 cubic meters and the cost of processed aluminum is 6210.00 dollars per cubic meter, how many dollars would be saved by changing the design of the can?

Answer 1

SOLUTION

Actual size of cans

Diameter (d) = 2.75 inches

Radius (r)

Height (h) = 5 inches

So,

Aluminium used in cans will be equal to total surface area(A) of cans

Now new cans designed with ratio d / h = 1

d = h

Let d = h = a

r = d / 2 = a / 2

Volume of cans is 12 oz

Converting oz to cubic inch

Volume of cans

Its value given above. put it

So d = h = 3.021 inches

Now total surface area(A) of cans

Amount of dollars would be saved = actual size can's area - new designed can's area