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Cricles; Area

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Cricles; Area

by gmattesttaker2 » Sun Mar 31, 2013 11:47 am
Hello,

Can you please help with this?

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?

Ans:[spoiler] squareroot (2/pi)[/spoiler]

I was just thinking though since the circular region is inside the square poster, can the radius of the circle not be 1 feet?

Thanks for your help,
Sri
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by rintoo22 » Sun Mar 31, 2013 12:12 pm
Square Region Area = 4
Circular Region Area = 2

2 = pi.(r^2) => r = (2/pi)^1/2.

Ok to answer your query " since the circular region is inside the square poster, can the radius of the circle not be 1 feet ".

I would say 'No'. However an expert opinion is required.
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by Anju@Gurome » Sun Mar 31, 2013 5:10 pm
gmattesttaker2 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 be the radius of the circular region in feet?
Area of the poster = 2² = 4 sq. feet
Hence, area of the circle = 2 sq. feet

If radius of the circle is r feet, the area of the circle is πr² sq. feet.
So, πr² = 2
--> r = √(2/π)
gmattesttaker2 wrote:... can the radius of the circle not be 1 feet?
No, it won't satisfy the given condition, i.e. 'area of the circular region is to be 1/2 the area of the poster'. In fact, 1 foot is the maximum possible radius of the circle.
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by Anju@Gurome » Sun Mar 31, 2013 5:11 pm
gmattesttaker2 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 be the radius of the circular region in feet?
Area of the poster = 2² = 4 sq. feet
Hence, area of the circle = 2 sq. feet

If radius of the circle is r feet, the area of the circle is πr² sq. feet.
So, πr² = 2
--> r = √(2/π)
gmattesttaker2 wrote:... can the radius of the circle not be 1 feet?
No, it won't satisfy the given condition, i.e. 'area of the circular region is to be 1/2 the area of the poster'. In fact, 1 foot is the maximum possible radius of the circle.
Anju Agarwal
Quant Expert, Gurome

Backup Methods : General guide on plugging, estimation etc.
Wavy Curve Method : Solving complex inequalities in a matter of seconds.

§ GMAT with Gurome § Admissions with Gurome § Career Advising with Gurome §
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