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# A certain dodgeball court is a circle with a square perfectly inscribe

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Math Expert
Joined: 02 Sep 2009
Posts: 51215
A certain dodgeball court is a circle with a square perfectly inscribe  [#permalink]

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17 Aug 2018, 10:11
00:00

Difficulty:

15% (low)

Question Stats:

83% (01:34) correct 17% (01:06) wrong based on 23 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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Re: A certain dodgeball court is a circle with a square perfectly inscribe  [#permalink]

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17 Aug 2018, 10:26
Bunuel wrote:
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) $$16\pi - 4\sqrt{2}$$

Required area= Area of circle- Area of inscribed square

Given ,area of square=16
So ,side of square=4
Hence diagonal of square =4*$$\sqrt{2}$$
Observation:-
Diameter of circle=diagonal of square
Or, radius of circle=1/2* diagonal of square=2*$$\sqrt{2}$$
So,area of circle=$$\pi$$*$$r^2$$=8$$\pi$$
So, required area=8$$\pi$$-16.

Ans. (D)
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PKN

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Re: A certain dodgeball court is a circle with a square perfectly inscribe &nbs [#permalink] 17 Aug 2018, 10:26
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