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505-555 Level|   Geometry|      
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Bunuel
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A certain dodgeball court is a circle with a square perfectly inscribe 02 Feb 2022, 04:45
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15% (low)

Question Stats:

86% (01:41) correct 14% (01:05) wrong based on 36 sessions

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A certain dodgeball court is a circle with a square perfectly inscribed inside it. The square represents the playing field, while the rest of the circle represents four rest areas for players. If the square has an area of 16, what is the area of the four rest areas combined?


A) \(4\pi − 16\)

B) \(8\pi\)

C) \(8\pi − 4\sqrt{2}\)

D) \(8\pi − 16\)

E) \(16\pi - 4\sqrt{2}\)
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D
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A certain dodgeball court is a circle with a square perfectly inscribe 02 Feb 2022, 04:59
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My Ans: (D) 8π -16

My Approach:

Shape: Square inscribed inside a circle

Area of square = 16
Therefore, side = 4

the diagonal of the square = diameter of circle = \(4\sqrt{2}\)

therefore, radius = \(2\sqrt{2}\)

Area of resting areas = Area of circle - area of square

\(= πr^2 - 16\)
= 8π -16
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A certain dodgeball court is a circle with a square perfectly inscribe 04 Feb 2022, 00:39
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Area of square =16
i.e side = 4; diagonal =4 sqrt2
Radius of circle = 2 sqrt 2

Now area of circle = pi*r*r = 8*pi

Area of sector = 8*pi/2 = 2*pi

Area of remaining circular area = 2*pi - 4

Area of all four = 8*pi -16

Hence Ans (D)
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