swerve wrote:
Square ABCD is perfectly inscribed in the circle pictured above. If minor arc AD measure 2Ï€, what is the approximate area of the shaded region?
A. 110
B. 72
C. 36
D. 18
E. 9
The OA is
D.
Please, can any expert explain this PS question for me? I have many difficulties to understand why that is the correct answer. Thanks.
The area of the shaded region = Area of the circle - Area of the square
Since the square is perfectly inscribed, Arc AD = Arc DC = Arc CB = Arc BA
Thus, length of arc AD = 1/4 of circumference of the circle
=> 2Ï€ = (2Ï€r)/4 => r = 4
=> Area of the circle = πr^2 = π.4^2 = 16π
Side of the square would be given by √2r
Area of the square = (Side)^2 = (√2r)^2 = 2r^2 = 2.4^2 = 32
Thus, the area of the shaded region = Area of the circle - Area of the square = 16Ï€ - 32 = 16.(3.14) - 32 = ~50 - 32 = ~18.
The correct answer:
D
Hope this helps!
-Jay
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