A geometry problem

Geometry Level 2

If x is the sum of the areas of the 2 congruent circles, and y is the area of the square, what is y/x in terms of π?

π/2 1 π 2/π

Ross Fasone by Ross Fasone , 21, USA

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2 solutions

x = 2 π r 2 a n d y = ( 2 r ) 2 = 4 r 2 \mathsf{x=2 \pi r^2}~and~y=(2r)^2=4r^2

y x = 4 r 2 2 π r 2 = 2 π \mathbf{\dfrac{y}{x}=\dfrac{4r^2}{2\pi r^2}}=\dfrac{2}{\pi}

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Consider 'a' as the diameter of the circles which corresponds the sides of the square. So, y = a*a,
and, x = 2 * ( pi * (a/2)^2 ), therefore, y/x = 2 / pi.

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