simple geometry with a sheet of paper
| Start with a regular sheet of paper, and divide it as shown, and let's pretend these subdivisions are squares, and the squares are 1x1 units.
what is the area? what is the perimeter? what is the length of the longest (straight) line I can draw on the sheet? | 
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| what is the area now? what is the perimeter? can you make a fold to make the area 10? what are the perimeters then? | 
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| How long is the fat line? | 
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| what is the volume? | 
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| what is the volume? | 
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| What is the volume? | 
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| what is the volume? suppose I fit a cone inside with the same base and height, what would be it's volume? | 
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| Suppose I cut the sheet along the blue line
what is the length of the blue line? what is the area of the left piece? | 
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| Now I roll this piece into a cone.
What is the area of the base of the cone? What is the volume of the cone? | 
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