## anonymous 5 years ago If you roll an 8.5-by-11-inch piece of paper into a cylinder by bringing the two longer sides together, you get a tall, thin cylinder. If you roll an 8.5-by-11-inch piece of paper into a cylinder by bringing the two shorter sides together, you get a short, fat cylinder. Which of the two cylinders has the greater volume?

1. anonymous

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.

2. anonymous

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?

3. anonymous

so B=pir3 right

4. anonymous

no the base is$B=\pi r^2$

5. anonymous

6. anonymous

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)?

7. anonymous

that mean 4.25

8. anonymous

wait how did you get 4.25?

9. anonymous

Here is a clue when you roll it the circumference ( 2 pi r) is 8.5 so no solve for r.

10. anonymous

now solve for r

11. anonymous

$2\pi r=8.5$

12. anonymous

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

13. anonymous

Next solve for the second volume. The circumference is going to be different.

14. anonymous

its not going to be 8.5 but what?

15. anonymous

$2pir=8.5$what that for

16. anonymous

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 $2 \pi r = 8.5$

17. anonymous

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?

18. anonymous

so that divde by 2pi

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