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Hikari93

  • 3 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?

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  1. dhatraditya
    • 3 years ago
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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.

  2. Romero
    • 3 years ago
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    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. Hikari93
    • 3 years ago
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    so B=pir3 right

  4. Romero
    • 3 years ago
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    no the base is\[B=\pi r^2\]

  5. Hikari93
    • 3 years ago
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    my bad what is radius if this

  6. Romero
    • 3 years ago
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    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. Hikari93
    • 3 years ago
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    that mean 4.25

  8. Romero
    • 3 years ago
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    wait how did you get 4.25?

  9. Romero
    • 3 years ago
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    Here is a clue when you roll it the circumference ( 2 pi r) is 8.5 so no solve for r.

  10. Romero
    • 3 years ago
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    now solve for r

  11. Romero
    • 3 years ago
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    \[2\pi r=8.5\]

  12. Romero
    • 3 years ago
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    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. Romero
    • 3 years ago
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    Next solve for the second volume. The circumference is going to be different.

  14. Romero
    • 3 years ago
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    its not going to be 8.5 but what?

  15. Hikari93
    • 3 years ago
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    \[2pir=8.5\]what that for

  16. Romero
    • 3 years ago
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    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. Romero
    • 3 years ago
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    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. Hikari93
    • 3 years ago
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    so that divde by 2pi

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