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# A circle with a radius of 6 has a square inscribed inside of it. What

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Manager
Joined: 26 Dec 2018
Posts: 142
Location: India
A circle with a radius of 6 has a square inscribed inside of it. What  [#permalink]

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11 Jan 2019, 06:47
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A circle with a radius of 6 has a square inscribed inside of it. What is the area of the black region?
Attachment:

01033-1.gif [ 3.23 KiB | Viewed 284 times ]

A) 23π - 31
B) 36π - 72
C) 63π - 42
D) 24π - 16
E) 30π - 62

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Re: A circle with a radius of 6 has a square inscribed inside of it. What  [#permalink]

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11 Jan 2019, 10:49
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UB001 wrote:
A circle with a radius of 6 has a square inscribed inside of it. What is the area of the black region?

A) 23π - 31
B) 36π - 72
C) 63π - 42
D) 24π - 16
E) 30π - 62

Area of black region = Area of O - Area of square

Side of a square will be 6$$\sqrt{2}$$, Since the present triangular region will be a 45-45-90

Area of black region = pi r^2 - s^2
36π - 72

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Re: A circle with a radius of 6 has a square inscribed inside of it. What  [#permalink]

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11 Jan 2019, 11:17
Are of shaded region= area of circle-area of square

Area of circle= pi*r^2= pi*6^2=36 pi
Side of square= 6*2^(1/2)
Thus,area of square= 72

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Re: A circle with a radius of 6 has a square inscribed inside of it. What  [#permalink]

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11 Jan 2019, 11:35
UB001 wrote:
A circle with a radius of 6 has a square inscribed inside of it. What is the area of the black region?
Attachment:
01033-1.gif

A) 23π - 31
B) 36π - 72
C) 63π - 42
D) 24π - 16
E) 30π - 62

Diagonal of the square = Diameter of the Circle

Or, $$a√2 = 12$$

Or, $$a^2 = 72$$

Area of the circle = $$πr^2$$

Or, Area of the circle = $$π6^2 = 36π$$

Thus, Area of the shaded region = $$36π - 72$$, Answer must be (B)
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Re: A circle with a radius of 6 has a square inscribed inside of it. What   [#permalink] 11 Jan 2019, 11:35
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