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Math Help - Hollow Cylinder volume

  1. #1
    Member mybrohshi5's Avatar
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    Hollow Cylinder volume

    Does anyone know the equation to find the volume of the solid material that makes up a hollow cylinder.

    I know the height, outer diameter, and thickness.

    What equation will give me the volume of just the material that makes up the hollow cylinder?


    Thank you
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  2. #2
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    Volume for a cylinder is V = \pi r^2h

    The volume you are taking about is the inner volume of your shape subtracted from the outer volume.

    You just need to find the two diameters/radui (outer and inner) to solve this problem. The Thickness should give you a good hint.

    So V = \pi r_\text{outer}^2h - \pi r_\text{inner}^2h
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  3. #3
    Member mybrohshi5's Avatar
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    That is how i did it but my teacher gave me an equation that is giving me different answers and im wondering if maybe i wrote the equation down wrong.

    This is for my physics lab and my teacher gave me this equation:

    [ 2(pi)(D)(T) - (pi)(T^2) ] x H

    This isnt giving me the same number though compared to finding it the way you mentioned.

    And the number isnt just a little different its like twice as large using that equation compared to if i find it the way you mentioned.
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  4. #4
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    What are your values for height thickness and outer diameter?

    (As mentioned in the first post)
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  5. #5
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    Quote Originally Posted by mybrohshi5 View Post
    Does anyone know the equation to find the volume of the solid material that makes up a hollow cylinder.

    I know the height, outer diameter, and thickness.

    What equation will give me the volume of just the material that makes up the hollow cylinder?


    Thank you
    You need the "mean" distance. Subtract the thickness from the outside diameter to get the inside diameter. If the outer radius is D/2, the thickness, T, then the inner radius will be (D/2)-T. Find the area of the annulus [ring] by finding the outside area and subtracting the inside circle area. Multiply by the length [height]. If you want to include the bottom, you'll have a circle of radius (D/2)-T. Multiply that by the thickness, T, for its volume.
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  6. #6
    Member mybrohshi5's Avatar
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    Quote Originally Posted by pickslides View Post
    What are your values for height thickness and outer diameter?

    (As mentioned in the first post)
    Height = 12.729 cm

    Diameter (outer) = 8.623 cm

    Thickness = 0.509 cm

    I get 342.4 cm^3 using the equation my teacher gave me but when i do it the way you meantioned i get 662.897 which is actually double not half like i thought.
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  7. #7
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     <br />
V =\pi r_\text{outer}^2h - \pi r_\text{inner}^2h= \pi \times 4.3115^2\times 12.729 - \pi \times 4.057^2\times 12.729 = \dots<br />
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  8. #8
    Member mybrohshi5's Avatar
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    Quote Originally Posted by pickslides View Post
     <br />
V =\pi r_\text{outer}^2h - \pi r_\text{inner}^2h= \pi \times 4.3115^2\times 12.729 - \pi \times 4.057^2\times 12.729 = \dots<br />

    opps i was using diameter when i got the 600 number.

    the V = 85.59

    the 12.729 was supposed to be 12.792

    but anyways why is this so much smaller than what i get using the equation my teacher gave me? Do you think i wrote it down wrong or can you see anything wrong with it that would fix my problem?

    Thank you
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  9. #9
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    Quote Originally Posted by mybrohshi5 View Post

    but anyways why is this so much smaller than what i get using the equation my teacher gave me? Do you think i wrote it down wrong
    Thank you
    Could be a reason.
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  10. #10
    Member mybrohshi5's Avatar
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    HMMM ok well thank you for your help
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  11. #11
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    File attached. Oops, missed a bracket.
    Attached Thumbnails Attached Thumbnails Hollow Cylinder volume-cylinder.jpg  
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