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?

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) (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 <---> ,
the green rectangles have .
For the rectangle to the left of all centers,
and for the one to the right of all centers,
.
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,
and .
So, according to the Pythagorean theorem,
the long leg measures

.
So the overall width encased in green (in cm) is
.
So I would say the width of the piece of paper has to be at least
or more realistically .
RELATED QUESTIONS
How many circles of radius 9 cm can be cut from a rectangular sheet 370 cm by 105... (answered by Cromlix)

I have the problem a rectangular piece of paper is three times as long as it is wide.... (answered by Alan3354)

How many circles of radius 5 cm can be cut from a piece of cartolina 63 cm by 78 cm?... (answered by Fombitz)

Five centimeters are cut off (along one side of) of a square sheet of paper and 8 cm are... (answered by Theo,ikleyn)

How many circles of radius 9 cm can be cut from a rectangular sheet 3.7 m by 1.05m? Thank (answered by Boreal,ikleyn)

a 48 cm wire is to be cut into two pieces. One piece must be 10 cm longer than the... (answered by cheesey)

An open box is to be made from a rectangular piece of tin that is 18 cm wide and 24 cm... (answered by Earlsdon)

a rectangular piece of paper has a length of 25cm and a breadth of 20 cm. The piece of... (answered by josgarithmetic)

Four squares, each with sides 4 cm long, are cut from the corners of a rectangular piece... (answered by checkley77)