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

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

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New post 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
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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New post 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

Answer B
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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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New post 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

Thus,area of shaded region= 36pi-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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New post 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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