Multiple choice

If the ratio of circumference of two circles is $4:9$, the ratio their area is:

  1. $9:4$
  2. $16:81$
  3. $4:9$
  4. $2:3$
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B Correct answer
Explanation

The ratio of the areas of two circles is the square of the ratio of their circumferences. Since the ratio of circumferences is 4:9, the ratio of their areas is 4^2 : 9^2, which is 16:81.

AI explanation

The ratio of the circumferences of two circles equals the ratio of their radii, so r1 divided by r2 equals 4 divided by 9. The ratio of their areas equals the square of the ratio of their radii, according to the area formula pi times r squared. Squaring the fraction 4/9 gives a ratio of 16 to 81.