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

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
An artist wishes to paint a circular region on a square post  [#permalink]

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07 Mar 2014, 04:51
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Difficulty:

5% (low)

Question Stats:

91% (01:06) correct 9% (01:25) wrong based on 587 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

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) $$\frac{1}{\pi}$$
(B) $$\sqrt{\frac{2}{\pi}}$$
(C) 1
(D) $$\frac{1}{\sqrt{\pi}}$$
(E) $$\frac{\pi}{2}$$

Problem Solving
Question: 141
Category: Geometry Circles; Area
Page: 80
Difficulty: 600

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Re: An artist wishes to paint a circular region on a square post  [#permalink]

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07 Mar 2014, 04:51
1
SOLUTION

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) $$\frac{1}{\pi}$$
(B) $$\sqrt{\frac{2}{\pi}}$$
(C) 1
(D) $$\frac{1}{\sqrt{\pi}}$$
(E) $$\frac{\pi}{2}$$

The area of the square poster = side^2 = 2^2 = 4.

The area of the circle must be half of that: $$\pi{r^2}=2$$ --> $$r=\sqrt{\frac{2}{\pi}}$$.

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Re: An artist wishes to paint a circular region on a square post  [#permalink]

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07 Mar 2014, 05:22
Area of the poster = 2*2 = 4

Let r be the radius of the circular region.

Per question, Pi(r)^2 = 4/2 = 2
r^2 = 2/pi
r = (2/pi)^1/2

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Joined: 04 Mar 2014
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Re: An artist wishes to paint a circular region on a square post  [#permalink]

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07 Mar 2014, 14:34
Donnie84 wrote:
Area of the poster = 2*2 = 4

Let r be the radius of the circular region.

Per question, Pi(r)^2 = 4/2 = 2
r^2 = 2/pi
r = (2/pi)^1/2

Exactly what I did.

B.
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Re: An artist wishes to paint a circular region on a square post  [#permalink]

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07 Mar 2014, 17:25
Option b.
Area of sq.=2*2=4
Area of circle=4/2=2
2=pi * r^2

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Math Expert
Joined: 02 Sep 2009
Posts: 58434
Re: An artist wishes to paint a circular region on a square post  [#permalink]

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08 Mar 2014, 13:46
SOLUTION

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) $$\frac{1}{\pi}$$
(B) $$\sqrt{\frac{2}{\pi}}$$
(C) 1
(D) $$\frac{1}{\sqrt{\pi}}$$
(E) $$\frac{\pi}{2}$$

The area of the square poster = side^2 = 2^2 = 4.

The area of the circle must be half of that: $$\pi{r^2}=2$$ --> $$r=\sqrt{\frac{2}{\pi}}$$.

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Intern
Joined: 24 Aug 2015
Posts: 7
Re: An artist wishes to paint a circular region on a square post  [#permalink]

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03 Oct 2015, 09:35
A circle is inside a square poster THAT IS 2 feet on a side meaning the square has a side of 2 feet each.
AREAcircle = 1/2AREAposter

Find AREA poster = s x s = 2 x 2 = 4
AREAcircle = (1/2)4 = 2
AreaCIRCLE = phi.r2
2 = phi.r2
2/phi = r2
r = \sqrt{2/phi}
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Re: An artist wishes to paint a circular region on a square post  [#permalink]

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19 Mar 2018, 16:19
Quote:

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) $$\frac{1}{\pi}$$
(B) $$\sqrt{\frac{2}{\pi}}$$
(C) 1
(D) $$\frac{1}{\sqrt{\pi}}$$
(E) $$\frac{\pi}{2}$$

The area of the poster is 4, so the area of the circle is 2. Thus:

πr^2 = 2

r^2 = 2/π

r = √(2/π)

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Re: An artist wishes to paint a circular region on a square post   [#permalink] 19 Mar 2018, 16:19
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