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Basic Math/Area of an ellipse/oval


In a work application, we have to squeeze a 5" round, flexible water pipe through a 4" opening.  No problem, just press down on the top, the circle becomes somewhat oval shape and it will fit in. I believe that this will reduce the area of the opening and, therefore, reduce the water flow rate, but my co-workers say I am wrong. They say that the circumference is the same, to which I agree, but I think the area of the opening has gotten smaller

If the pipe were 5"x5" SQUARE (36si) and the sides were changed by one inch to be a 6"x4" SQUARE(24si), the area inside the square would be reduced.  Wouldn't that be the same for a circle to an oval?  

Am I correct and is there a formula that can prove this ?

Thanks, Jeffrey

Hello Jeffrey,

Your instinct is correct.  Given a length of string tied at both ends, a loop, a perfect
circle maximizes the area formed.

You can see this with your example.  Take your water tubing, with a 5" diameter, and crush it
so it is flat.  The circumference is the same as when not crushed or deformed, but clearly now
the cross sectional area is zero (or close to it)!


A. Mantell  

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Abe Mantell


Hello, I am a college professor of mathematics and regularly teach all levels from elementary mathematics through differential equations, and would be happy to assist anyone with such questions!


Over 15 years teaching at the college level.

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B.S. in Mathematics from Rensselaer Polytechnic Institute
M.S. (and A.B.D.) in Applied Mathematics from SUNY @ Stony Brook

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