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A square is inscribed in a circle. If the side of the same square 4cm,

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A square is inscribed in a circle. If the side of the same square 4cm,  [#permalink]

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New post Updated on: 15 Jan 2019, 09:34
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A square is inscribed in a circle. If the side of the same square is 4cm, what is the area of the circle?

A. 2π
B. 4π
C. 6π
D. 8π
E. None of these

Originally posted by akurathi12 on 15 Jan 2019, 08:21.
Last edited by Bunuel on 15 Jan 2019, 09:34, edited 1 time in total.
Edited the OA.
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Re: A square is inscribed in a circle. If the side of the same square 4cm,  [#permalink]

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New post 15 Jan 2019, 08:34
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akurathi12 wrote:
A square is inscribed in a circle. If the side of the same square is 4cm, what is the area of the circle?

A. 2π
B. 4π
C. 6π
D. 8π
E. None of these


Sides of the square is 4 units, so Diagonal of the square must be \(4\sqrt{2}\)

Diagonal of the square = Diameter of the Circle = \(4\sqrt{2}\)

So, Radius of the CIrcle is \(2\sqrt{2}\)

Thus, Area of the Circle must be \(π*2\sqrt{2}*2\sqrt{2} = 8π\), Answer must be (D)
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Re: A square is inscribed in a circle. If the side of the same square 4cm,  [#permalink]

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New post 15 Jan 2019, 08:37
akurathi12 wrote:
A square is inscribed in a circle. If the side of the same square is 4cm, what is the area of the circle?

A. 2π
B. 4π
C. 6π
D. 8π
E. None of these


OP is the answer correct, i am getting D.

side = 4
diagonal = 4 \(\sqrt{2}\)
radius = 2 \(\sqrt{2}\)

Area = 8π

Do share your thoughts on this.
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Re: A square is inscribed in a circle. If the side of the same square 4cm,  [#permalink]

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New post 15 Jan 2019, 09:26
Can anyone explain why it is 6pie rather than 8pie..?

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A square is inscribed in a circle. If the side of the same square 4cm,  [#permalink]

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New post Updated on: 15 Jan 2019, 09:54
HarikaBurlakanti wrote:
Can anyone explain why it is 6pie rather than 8pie..?

Posted from my mobile device


OA Was wrong, it is indeed D.
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Originally posted by KanishkM on 15 Jan 2019, 09:31.
Last edited by KanishkM on 15 Jan 2019, 09:54, edited 1 time in total.
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Re: A square is inscribed in a circle. If the side of the same square 4cm,  [#permalink]

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New post 15 Jan 2019, 09:51
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OA for the question must be (D) post has been modified by ADMIN member, Bunuel...
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Re: A square is inscribed in a circle. If the side of the same square 4cm,  [#permalink]

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New post 15 Jan 2019, 09:55
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Re: A square is inscribed in a circle. If the side of the same square 4cm,  [#permalink]

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New post 16 Jan 2019, 01:03
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side^2 = (diagonal^2)/2

side = 4
diagonal = 4√2
radius = 2√2

Area = 8π
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Re: A square is inscribed in a circle. If the side of the same square 4cm,  [#permalink]

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New post 16 Jan 2019, 01:52
1
akurathi12 wrote:
A square is inscribed in a circle. If the side of the same square is 4cm, what is the area of the circle?

A. 2π
B. 4π
C. 6π
D. 8π
E. None of these


Check this post for relations of regular polygons inscribed in circles: https://www.veritasprep.com/blog/2013/0 ... relations/

When a square is inscribed in a circle,
\(r:a = 1:\sqrt{2}\)

\(r/4 = 1:\sqrt{2}\)

\(r = 2*\sqrt{2}\)

Area of circle \(= \pi*r^2 = \pi*(2*\sqrt{2})^2 = 8\pi\)

Answer (D)
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Re: A square is inscribed in a circle. If the side of the same square 4cm,  [#permalink]

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New post 16 Jan 2019, 03:26
akurathi12 wrote:
A square is inscribed in a circle. If the side of the same square is 4cm, what is the area of the circle?

A. 2π
B. 4π
C. 6π
D. 8π
E. None of these


diameter of circle = diagonal of square = 4 srt 2
radius = 2 sqrt 2
area : (2 sqrt 2)^2 * pi
: 8 pi
IMO D
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Re: A square is inscribed in a circle. If the side of the same square 4cm,  [#permalink]

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New post 17 Jan 2019, 17:57
akurathi12 wrote:
A square is inscribed in a circle. If the side of the same square is 4cm, what is the area of the circle?

A. 2π
B. 4π
C. 6π
D. 8π
E. None of these



Since the square is inscribed in the circle, the diagonal of the square is equivalent to the diameter of the circle. Thus, 4√2 = diagonal of square = diameter of circle.

So the radius is half the diameter, or 2√2, and thus the area is (2√2)^2 x π = 8π.

Answer: D
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Re: A square is inscribed in a circle. If the side of the same square 4cm,   [#permalink] 17 Jan 2019, 17:57
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