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Topic: Intersection of Cylinders
Replies: 3   Last Post: Apr 23, 2005 11:43 AM

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Posts: 10
Registered: 4/21/05
Re: Intersection of Cylinders
Posted: Apr 22, 2005 10:14 AM
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"Paul Ciszek" <> wrote in message
> Picture two Cylinders of radius r that intersect at right angles.
> The volume common to both cylinders is a funny looking shape that
> is round in cross section in two directions and square in the third.
> It will smoothly roll in two orthogonal directions.

> I tried to find the volume of this shape, and I get 16r^3/3.
> I would have expected pi to turn up in there somewhere, but
> it doesn't.

No, it doessn't. The volume is the sum of rectangular slices. So, no Pi.
[ If the cylinders are: x^2 + z^2 = a^2 ; y^2 + z^2 = a^2 ,
Then the plane: z = c where ( -a .LE. c .LE. a )
is a rectangular cut of the solid of intersection. ]

> Does this shape have a name?

> The shape formed by the intersection of *three* cylinders at right
> angles is even cuter. Does it have a name? Has anyone sketched
> the shapes produced by cylinders intersecting along other axes,
> such as the four diagonals of a cube?

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