Sonalika42 wrote:
ABCD is a square and AEC and AFC are one fourth of the circumference of the circle whose radius is equal to the length of the side of the square ABCD. Ratio of unshaded to shaded region? image is attached below
(A) 22 : 3
(B) 4 : 3
(C) 3 : 4
(D) 7 : 4
(E) cannot be determined
Join AC, it divides the square into 2 equal parts..
Let us take one part ABFC, ABC is isosceles right angled triangle with sides, say 2, so area = (1/2)*2*2=2
Area of ABFC.. ABFC is 1/4th of a circle with side 2, so area = \(\frac{\pi*2^2}{4}=\pi\)
so shaded portion = area of ABFC - area of ABC = \(\pi-2\)
But there are two shade portion, one each side of AC, so area = 2(\(\pi-2\))=\(2\pi-4\)
therefore, the area of unshaded portion = area of square - area of shaded portion = \(2*2-2(\pi-2)=4-2\pi+4\)=\(8-2\pi\)
Ratio unshaded to shaded = \(8-2\pi\):\(2\pi-4\)=\(4-\pi\):\(\pi-2\)=\(\frac{6}{7}:\frac{8}{7}=6:8=3:4\)
C
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