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The ratio of the areas of two circles is 9:4. If the circumference of the smaller circle is 20\pi, what is the perimeter of the larger circle?

(A) 13\pi

(B) \frac{40\pi }{3}

(C) \frac{90\pi }{3}

(D) 30\pi

Thanks

miranda

10-10-2013, 11:55 AM

The ratio of the areas of two circles is 9:4 \frac{A_{1}}{ A_{2}}=\frac{\pi (r_{1})^2}{\pi (r_{2})^2}=\frac{ (r_{1})^2}{ (r_{2})^2}=\frac{9}{4} \Rightarrow \frac{ r_{1}}{ r_{2}}=\frac{3}{2} \Rightarrow r_{1}= r_{2} \frac{3}{2}

The circumference of the smaller circle is given by the formula P_{2}=2\pi r_{2}=20\pi \Rightarrow r_{2}= 10 \ units

The circumference of the larger circle is given by the formula P_{1}=2\pi r_{2} \frac{3}{2}=2\pi 10 \frac{3}{2}=30\pi \ units

Therefore the correct answer is (D).

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