Oval Area
Posted March 29, 2011
By admin
Oval Area
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Lawn area at Adelaide Oval
How to find the area of moss's egg (Egg shaped oval created from overlapping circles)?
For my math project I need to find the area of 'Moss's egg'
This website has a picture of what im finding - http://mathworld.wolfram.com/MosssEgg.html
The two larger circles have a radius of 6cm
I have lengths for most of the other lines just ask if you need them!
Thanks!
You need to know the distance between the two large circle centres.
If this is x then the lower part of the egg is a semi-circle with radius 6 - x/2 so area(1/2)*pi*(6 - x/2)^2
The portion each side is 1/8th of a circle with radius 12 - x. They each have an area (1/8)*pi*(12 - x)^2 but you must subtract the overlap which is a right triangle of area
(6 - x/2)^2.
The upper small part is a quarter circle with radius
12 - x - sqrt2*(6 - x/2) = (2 - sqrt2)(6 - x/2)
so its area is
(1/4)*pi*(2 - sqrt2)^2*(6 - x/2)^2 = (3/2 - sqrt2)*pi*(6 - x/2)^2
Putting it all together you get
Area of egg = (3*pi - sqrt2*pi - 1)*(6 - x/2)^2
P.S. I did this rather quickly so there may be a numerical slip but I think that it is essentially correct.
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