SOLUTION: Consider what happens when the sides of an 8.5x11 inch piece of paper are taped to form a cylinder. If it is possible, design a rectangular piece of paper with the same area sot ha

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Question 930731: Consider what happens when the sides of an 8.5x11 inch piece of paper are taped to form a cylinder. If it is possible, design a rectangular piece of paper with the same area sot hat the volume of one of the cylinders is double the volume of the other cylinder and explain how you found them. If it is not possible, explain why not.
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
You need to choose which side on the original paper you want to curve to form the circumference. I am choosing the 11 inch direction.

2pi%2Ar=11
r=11%2F%282pi%29
volume, %288.5%29pi%2Ar%5E2=%288.5%29pi%2811%2F%282pi%29%29%5E2=8.5%28121%2F%284pi%29%29


You want another rectangle, dimensions x and y so that xy=%288%261%2F2%29%2811%29.
The volume must be double of that from the 8.5x11 form.
Circumference, using y, re-using r as if it were a NEW variable unequal to what/how was previously used,
2pi%2Ar=y
r=y%2F%282pi%29
Again using x as the "height" for the cylinder,
volume, x%2Api%2Ar%5E2=x%2Api%28y%2F%282pi%29%29%5E2=x%2Api%28y%5E2%29%281%2F4%29%281%2Fpi%29%5E2
volume, %28x%2Ay%5E2%29%2F%284pi%29.
NOW, use the xy area to eliminate one of the dimensional variables. Remember you want the volume here to be TWICE that formed from the 8.5x11 paper.

(unfinished here)