how many cases?

Question

The U.S consumes 2.6 billion cases per yr. If ea. Case holds 24-1/2 liter bottles. ea. case is 1o.2' tall, 15.1' long, 8.3' wide.if lined up at equator. how many times would they go around the earth? What's perimeter, area of all cases together?the volume? Circumference of earth Equator =24,901 miles. 1 mile=5280 ft. Plz show work

Answer 1

First things first. The case dimensions should be inches, not feet. If they were feet you would be able to get many thousands of bottles in the case, not just 24.
So I'll assume the dimensions are inches. The cases can be laid in three different ways, so for starters we'll calculate by their length, 15.1 inches.
Number of cases fitting around the earth if they're packed end to end: 24901*5280*12/15.1=1.04485*10^8.
Therefore 2.6*10^9 cases would girdle the earth 2.6*10^9/1.04485*10^8=24.88 times.
If the cases are side by side (8.3in apart) this changes to 24.88*8.3/15.1=13.8 times; and if 10.2in apart=16.81 times, because more cases can girdle the earth if packed differently.
The volume of one case is 15.1*10.2*8.3=1,278.366 cu in=0.74 cu ft. 1.04485*10^8*1278.366=total volume of cases placed lengthwise=7.76*10^7 cu ft.

Comments

If all of these cases were lined up end to end at the equator, how many times would they go around the earth? Perimeter & area of the bases of all cases together?  The volume? And yes it would 1st b converted to in. Thx!

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I've adjusted the wording slightly to say the cases are packed end to end just to clarify the calculation; the total volume of the cases so packed is at the end of the answer, but I didn't work out the perimeter and area because I wasn't sure what needed to be included or how these were to be defined. You may be able to calculate for yourself these quantities given the info already calculated in the answer.