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# A square is inscribed in a circle, which in turn is circumscribed by a

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Director
Joined: 22 Feb 2018
Posts: 601
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20 Nov 2019, 22:34
00:00

Difficulty:

75% (hard)

Question Stats:

44% (03:26) correct 56% (03:39) wrong based on 16 sessions

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A square is inscribed in a circle, which in turn is circumscribed by another square as shown (figure not drawn to scale). If the area of the circle is 64π square centimeter, the area of the shaded portion will be:

Refer the attached figure.

A) 8π
B) 16
C) 12π
D) 32
E) 48

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Square -circle- square.jpg [ 17.49 KiB | Viewed 265 times ]

Senior Manager
Joined: 16 Feb 2015
Posts: 355
Location: United States
A square is inscribed in a circle, which in turn is circumscribed by a  [#permalink]

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21 Nov 2019, 21:19
Raxit85 wrote:
A square is inscribed in a circle, which in turn is circumscribed by another square as shown (figure not drawn to scale). If the area of the circle is 64π square centimeter, the area of the shaded portion will be:

Refer the attached figure.

A) 8π
B) 16
C) 12π
D) 32
E) 48

Area of Circle = 64π
π*r^2 = 64π
r^2=64; r=8. dia= 16.
For a small square, it will be the diagonal length, so side will be = 16/√2
For a large square, it will be side. i.e 16

So Area of shaded region= 1/4 * [ { 64π - (16/√2)^2 } + { (16^2) - 64π } ]
= 32---- IMO D

Please provide kudos, if you find my explanation good Enough
A square is inscribed in a circle, which in turn is circumscribed by a   [#permalink] 21 Nov 2019, 21:19
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