SOLUTION: If one were to cut five circles, each 2 cm in diameter, from a rectangular piece of paper 6 cm long, at least how many cm’s wide would the piece of paper have to be?

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Question 1061893: If one were to cut five circles, each 2 cm in diameter, from a rectangular piece of paper 6 cm long, at
least how many cm’s wide would the piece of paper have to be?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
Here are 5 circles (with their centers) packed as tightly as I can pack them:
If each circle has diameter=2cm <---> radius=1cm ,
the green rectangles have length=6cm .
For the rectangle to the left of all centers,
and for the one to the right of all centers,
width=1cm .
As for the (middle) green rectangle going through all the circle centers,
looking at the red equilateral and right triangles
we can calculate its width.
For the right triangles,
hypotenuse=2cm and shortleg=1cm .
So, according to the Pythagorean theorem,
the long leg measures
sqrt%28%282cm%29%5E2%2B%281cm%29%5E2%29=sqrt%283%29cm .
So the overall width encased in green (in cm) is
1%2B1%2Bsqrt%283%29=highlight%282%2Bsqrt%283%29=about3.732%29 .
So I would say the width of the piece of paper has to be at least
highlight%283.74cm%29 or more realistically highlight%283.8cm%29 .