Multiple choice

The areas of two circles are in the ratio $121:49$. Find the ratio of their circumferences.

  1. $\pi$
  2. $\displaystyle\frac{12\pi}{3}$
  3. $\displaystyle\frac{11}{7}$

  4. None
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C Correct answer
Explanation

The ratio of areas of two circles is (r1/r2)^2 = 121/49. Thus, the ratio of radii r1/r2 = 11/7. Since circumference is 2*pi*r, the ratio of circumferences is also 11/7.

AI explanation

The area of a circle is pi times the radius squared, so the ratio of the radii is the square root of the ratio of their areas. Taking the square root of the area ratio 121 to 49 gives a radius ratio of 11 to 7. Because the circumference is 2 pi r, the ratio of the circumferences is identical to the ratio of the radii, which is 11 to 7, or 11 divided by 7.

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