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Math Help - Cylinder Problem

  1. #1
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    Cylinder Problem

    I have a maths question that I can't solve. It reads as follows:

    "A small cylinder is placed on the top of two identical cylinders, which are touching each other as shown in the diagram. Find the radius of the small cylinder."

    The diagram can be seen here:Cylinder Problem-cyclinder.png



    Can anyone please help me solve this as I have no idea!? Also could you please post any working with it?
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  2. #2
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    Re: Cylinder Problem

    Quote Originally Posted by hholbrook View Post
    I have a maths question that I can't solve. It reads as follows:

    "A small cylinder is placed on the top of two identical cylinders, which are touching each other as shown in the diagram. Find the radius of the small cylinder."

    The diagram can be seen here:Click image for larger version. 

Name:	cyclinder.png 
Views:	20 
Size:	14.8 KB 
ID:	22549

    Can anyone please help me solve this as I have no idea!? Also could you please post any working with it?
    1. I've modified your sketch a little bit (see attachment)

    2. The radius of one of the bigger pipes is R = 3, the radius of the smaller pipe is r. h and the 2 radii form a right triangle:

    h^2 = (3+r)^2-3^2 = r(6+r)~\implies~h=\sqrt{r(6+r)}

    3. The total height of the bundle of pipes is 9:

    9 = r+h+3 = r+\sqrt{r(6+r)}+3

    4. Solve for r.
    Spoiler:
    You should come out with r = 2
    Attached Thumbnails Attached Thumbnails Cylinder Problem-dreizylinder.png  
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