Question 478522: The circle O having diameter of 2cm,has a square inscribed in it .Each side of the square is then taken as a diameter to form 4 small circles O”. find total area of all four O” circles which is outside the circle O.
Answer by cleomenius(959)   (Show Source):
You can put this solution on YOUR website! The first thing I did was to find the side of the square inscribed in the circle,
as the diameter of the circle will be the diagonal of the square, this will form two 45 45 90 right triangles with a hypotenuse of 2.
Since s = ssqrt(2), 2 = s(sqrt(2).
divide 2 by sqrt(2) = 2/sqrt(2)
Multiply the numerator and denominator by sqrt(2) to obtain 2(sqrt(2)/2 for each side of the square, or sqrt(2)
Now, these are being used as diameters for four more circles, so we determine the radius of each one of the four to be sqrt(2)/2
So this value squared times pi will be the area of each circle, or 2/4 = 1/2 times pi = 1/2 pi for each circle times four circles results in 2 pi as the area for the four circles combined.
The area of the original circle is pi r^2, radius being 1 so the area of the original circle will come to 1pi.
So, since the outer circles obviously cover the original circle completely, the area outside the original should be 2pi minus pi, or one pi.
Cleommenius.
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