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2010 AMC 10A Problem 5

Problem 5 of 25EasierGeometry

The area of a circle whose circumference is 24π24\pi is kπ.k\pi. What is the value of k?k?

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Solution

Recall that the formula for the circumference of a circle is 2πr.2 \pi r. We then have that 24π=2πr 24\pi = 2\pi r r=12. r = 12. The area of a circle is πr2,\pi r^2, so we have that kπ=π122 k \pi = \pi 12^2 k=144. k = 144. Thus, E is the correct answer.

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Concepts: circumference · circle area

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