SOLUTION: Ms.Ikelyn, I asked a question here: https://www.algebra.com/tutors/students/your-answer.mpl?question=1204433 To which you responded (with a helpful!) lesson about a TWIN probl

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: Ms.Ikelyn, I asked a question here: https://www.algebra.com/tutors/students/your-answer.mpl?question=1204433 To which you responded (with a helpful!) lesson about a TWIN probl      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1204467: Ms.Ikelyn,
I asked a question here: https://www.algebra.com/tutors/students/your-answer.mpl?question=1204433
To which you responded (with a helpful!) lesson about a TWIN problem. However, I am confused and need help. What is that "shift" term? And can you break it down simpler?
Thank you Ma'am
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!



Let us assume these bottles are circles with radius 5cm for simplicity.
The densest possible packing is hexagonal packing for circles, as shown below:
HJh78

For the first layer, we find that the maximum amount of spheres we can fit on the first layer is 1000%2F%285%2A2%29=100+circles.
Since the second layer is in between the circles, one can only fit 99 circles. The third layer can fit another 100+circles and so on.
Then, we can build an equilateral triangle and show that every stack increases the width of the area filled by
r%2Asqrt%283%29=5sqrt%283%29
Given the first layer has a thickness (remember, circle represents bottles) of 10cm, the amount of layers that can be fitted is the floor of
%28%281000-10%29%2F%285sqrt%283%29%29%29%2B1=115.3153532995459 or 115 layers.
since first two layers have %28100%2B99%29+circles, and there is 115%2F2=57.5, means 57*first two layers have %28100%2B99%29 and .5=1%2F2 means we take one more first layer which is 100
This can be formed into
57%28100%2B99%29%2B100+=11443 circles, in your case bottles.
answer: 11443 bottles