A square of circle

Geometry Level 2

There are two circles of different sizes, the smaller circle has a radius of 5. The numerical value of the square of the area of the smaller circle is equal to the numerical value of the area of the larger circle. Find the radius of the larger circle.

Give your answer to 3 decimal places.


The answer is 44.311.

Kaleem Kħặŋ by Kaleem Kħặŋ , 26, Pakistan

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2 solutions

Pham Khanh
Sep 29, 2016

Call the smaller circle's radius r r ; larger circle's radius R R . We have: ( π r 2 ) 2 = π R 2 (\pi r^2)^2=\pi R^2 ⟺ π 2 r 4 = π R 2 \iff \pi^2 r^4=\pi R^2 ⟺ π r 4 = R 2 \iff \pi r^4=R^2 ⟺ R = π r 4 = r 2 π = 25 π ≈ 44.311 \iff R=\sqrt{\pi r^4}=r^2 \sqrt{\pi}=25 \sqrt{\pi} \approx \boxed{44.311}

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Let R R be the radius of the bigger circle, then we have

[ π ( 5 2 ) ] 2 = π R 2 [\pi(5^2)]^2=\pi R^2

R ≈ 44.311 c m R\approx \boxed{44.311~cm}

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