12 replies to this topic

[BMAD]

Your child needs help. He needs to cut out 10 circles. Upon measuring the circle size he needs, you find the radius of the circle to be 2.5 inches. Assuming that a sheet of paper is only 8.5x11 what is the minimum number of sheets of paper needed to make the circles?

[bonanova]

Spoiler for Looks like

Five sheets. Only two 5" circles would fit on a sheet.

If the diameter were 2.5" you could fit them all on a single sheet.

[bgm1961]

Assuming you can tape the sheets together, the answer is:

 

Spoiler for

Three sheets if you tape them together before plotting the circles. Three sheets taped togther would provide a canvas 11" x 25.5" .... large enough to plot two rows of five circles, 5" in diameter.

Edited by bgm1961, 20 February 2013 - 06:32 PM.

[TimeSpaceLightForce]

Spoiler for project

5 circles makes a ball with 10 different colored circles

[BMAD]

Still haven't found the answer I am looking for

[bonanova]

By circle, which is a locus of points, we assume you mean disc, which includes the interior points.

[Prime]

Spoiler for Just 2 per page

Cannot fit more than two 2.5-inch radius holes into an 8.5x11 in page.

Using a glue or scotch tape would be a different project.

[BMAD]

Spoiler for Just 2 per page

Cannot fit more than two 2.5-inch radius holes into an 8.5x11 in page.
cirlesinsheet.gif
Using a glue or scotch tape would be a different project.

I agree with the picture but you are missing something...something obvious

[bgm1961]

I guess I/we are missing something obvious, then.  Because from strictly an area calculation, at least three sheets of paper are needed.

 

The combined area of 10 circles with a 2.5" radius is 196.25 sq in. The combined area of TWO 8.5 x 11 sheets of paper is 187 sq in. So no matter how many arcs you divide each circle in order to maximize the coverage of a piece of paper, you'll need AT LEAST three sheets of paper to meet the area requirements alone. As I mentioned In my earlier post, the project can be completed with three sheets of paper.

[bgm1961]

Another way of tackling the problem requires challenging the wording of the puzzle. Nothing in the wording specifies the formation of the circle. I.e., are the circles DISCS or RINGS?  Answers provided thus far assume the circles are to be shaped as discs. But if they can be rings, then only one sheet of paper is needed.

 

If the "circles" can be rings, here's how it can be done with one sheet of paper. Rather obvious but I like to spell things out anyway:

 

Spoiler for

  Position one sheet of paper in the "portrait" orientation and cut it into horizontal strips (at least 20).  The circumfance of a 2.5" radius circle is 15.7". So working with the 20 strips of paper each 8.5" long, you'll need two strips to form a ring 5" in diamter. Its a simple matter to tape two strips together on both ends to form a 5" diameter ring... err, circle.