



 
Hi Margaret. The cardboard pattern will be curved, you are right. Take a look at this similar problem with diagrams that I solved awhile ago: Here's the math for your situation, based on the analysis and diagrams in that earlier problem: The important results are: radius of the outer circle of the pattern is 10.9252, radius of the inner circle is 3.2022 and the angle is 208 degrees. Thus, the appropriate shape is this: To make this pattern on cardboard, I'll first figure out the overall height: And of course the width is just the outside diameter, so the width is 2(10.9252) = 21.8904. So cut a cardboard rectangle 21.8904 by 12.7858 inches (round this off as you see fit!), then locate the center of the circles by going to the middle of the sheet left/right, and drop down from the top 10.9252 inches. Use a compass (use string if you don't have a compass) and draw the outside circle using the radius 10.9252 inches. Then draw the inside circle with radius 3.2022 inches. Finally draw straight cut lines from the center to the point where the outside circle touches the bottom of the cardboard.
Then cut out your pattern and roll it up. Please do email us a photo of the cupcake when you have it put together! Hope this helps,
 


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