Intersecting Circles
In the diagram below, the radius of the larger circle is 20 and the radius of the smaller circle is 15 (not drawn to scale). The illustrated radii are at right angles.
What is the difference of the areas of the non-overlapping portions?
What is the difference of the areas of the non-overlapping portions?
posted by Zaux at
6:56 AM
9 Comments:
I'm reluctant to post this, because it seems too simple and it's probably wrong, but isn't it the same as the difference between the areas of the complete circles??
Area of large circle = 1256.637061 units
Area of small circle = 706.8583471 units
Difference = 549.7787139 units.
The shared portion in the centre is the same area deducted from the total area of each circle, so the difference between them is the same whether we take account of the shared section or not
Please be right....
Please be right.....
Please be right.....
Please be right.....
:-)
Confirmed.
deltaA=(Alarge-shared)-(Asmall-shared)
deltaA=Alarge-shared-Asmall+shared
deltaA=Alarge-Ashared
Alarge=Pi*20^2
Asmall=Pi*15^2
delta=Pi*(20^2-15^2)=175*Pi
For a tough problem, figure out the shaded area
Cam
"deltaA=Alarge-Ashared" should be
"deltaA=Alarge-Asmall"
Cam
Hi Dual ...
you are right man ... as Cam has already acknowledged
Woohoo!
Credibility restored (a little).
Now if there was a prize hidden behind one of those circles, and you asked me to choose.....Oh no, wrong puzzle, I was rubbish at that one!!
This post has been removed by the author.
I get this.
Non overlapping area of large circle is 1090.5952
Non overlapping area of small circle is 540.8165
Overlapping area 166.0419
...difference of the areas of the non-overlapping portions?
549.7787
Confirmed area of shared portion.
integral of(sqrt(20^2-x^2)-(25-sqrt(15^2-x^2)) from x=-12 to 12
-12 and 12 are the intersections
A~=166.042
Cam
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