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visualize the problem, find out the perimeter of the circle formed by joining the two edges in both cases. you will get the radius that way.
Do you know the formula in finding the volume of cylinder? Its the B * H but in this case the B is circular so its the area of a circle Pi r^2 * H you know if you roll it the long way you have a height of 11 and if you roll it the other way you have a H of 8.5 so no you have Pi r^2 * 11= Volume in the long way Pi r^2 * 8.5= Volume the short way Now you need to find the radius. Can you think of a way in finding the radius?
so B=pir3 right
no the base is\[B=\pi r^2\]
my bad what is radius if this
Lets say you roll it up the long way with the H=11 when you roll it you can see the base right? Can you make a connection between the base and the width of the paper (8.5)?
that mean 4.25
wait how did you get 4.25?
Here is a clue when you roll it the circumference ( 2 pi r) is 8.5 so no solve for r.
now solve for r
now that you have that and now you can figure out what r is plug it back to the volume equation and thats the first volume
Next solve for the second volume. The circumference is going to be different.
its not going to be 8.5 but what?
\[2pir=8.5\]what that for
You know what's the circumference right? the length around a circle. Because you rolled up the paper the length of 8.5 becomes the circumference the formula for the circumference is 2 Pi r and you know that the circumference is 8.5 so \[2 \pi r = 8.5\]
solve for r and that the radius of the circle or the base. But you want the area of the base so plug that in to the original Volume formula got it?
so that divde by 2pi