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An artist wishes to paint a circular region on a square post

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An artist wishes to paint a circular region on a square post [#permalink] New post 07 Oct 2005, 06:48
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89% (01:46) correct 10% (00:31) wrong based on 47 sessions
An artist wishes to paint a circular region on a square poster that is 2 feet on a side. If the area of the circular region is to be 1/2 the area of the poster, what must be the radius of the circular region in feet?

(A) 1/pi
(B) sqrt(2/pi)
(C) 1
(D) 2/sqrt(pi)
(E) pi/2
[Reveal] Spoiler: OA

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Last edited by Bunuel on 17 Mar 2013, 23:54, edited 1 time in total.
Edited the question and moved to PS forum.
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 [#permalink] New post 07 Oct 2005, 07:10
Area of the poster is 2x2 = 4

1/2 the area = 2

pi*r^2 = 2

r^2 = 2/pi

r = sqrt(2/pi) answer (B)

Watchout b/c the answers are trying to fool you into choosing the largest circle that would fit into the circle which would be 2/sqrt(pi). DOn't forget to divide the area of the poster in half.

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 [#permalink] New post 07 Oct 2005, 07:27
it's a clear B for me (same way as brian)
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Re: An artist wishes to paint a circular region on a square [#permalink] New post 17 Mar 2013, 23:48
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étudiant wrote:
An artist wishes to paint a circular region on a square poster that is 2 feet on a side. If the area of the circular region is to be 1/2 the area of the poster, what must the radius of the circular region in feet?

(A) 1/pi
(B) sqrt(2/pi)
(C) 1
(D) 2/sqrt(pi)
(E) pi/2

Please explain your answer.


Responding to a pm:

The side of the square is 2 feet so area of the square poster is 4. The artist can paint the circle anywhere on the poster - the only thing is that the area of the circle must be 4/2 = 2 = \pi*r^2 i.e. r must be \sqrt{\frac{2}{\pi}}

The diameter of a circle is equal to the side of the square only if the circle is inscribed in the square i.e. the circle touches all the four sides of the square. Here, the problem doesn't say that the circle must be inscribed in the square - it only says that it must be drawn somewhere in the square and its area must be half of the area of the square.
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Re: An artist wishes to paint a circular region on a square [#permalink] New post 18 Mar 2013, 05:40
VeritasPrepKarishma wrote:
étudiant wrote:
An artist wishes to paint a circular region on a square poster that is 2 feet on a side. If the area of the circular region is to be 1/2 the area of the poster, what must the radius of the circular region in feet?

(A) 1/pi
(B) sqrt(2/pi)
(C) 1
(D) 2/sqrt(pi)
(E) pi/2

Please explain your answer.


Responding to a pm:

The side of the square is 2 feet so area of the square poster is 4. The artist can paint the circle anywhere on the poster - the only thing is that the area of the circle must be 4/2 = 2 = \pi*r^2 i.e. r must be \sqrt{\frac{2}{\pi}}

The diameter of a circle is equal to the side of the square only if the circle is inscribed in the square i.e. the circle touches all the four sides of the square. Here, the problem doesn't say that the circle must be inscribed in the square - it only says that it must be drawn somewhere in the square and its area must be half of the area of the square.


Amazing explanation ... thanks Karishma :)
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Re: An artist wishes to paint a circular region on a square   [#permalink] 18 Mar 2013, 05:40
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