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...

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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. \(\dfrac{1}{\pi}\)

B. \(\sqrt{\dfrac{2}{\pi}}\)

C. \(1\)

D. \(\dfrac{1}{\sqrt{\pi}}\)

E. \(\dfrac{\pi}{2}\)

OA B

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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. \(\dfrac{1}{\pi}\)

B. \(\sqrt{\dfrac{2}{\pi}}\)

C. \(1\)

D. \(\dfrac{1}{\sqrt{\pi}}\)

E. \(\dfrac{\pi}{2}\)

OA B

Solution:

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)

Answer: B