Multiple choice

The areas of two circular fields are in the ratio $16 : 49$. If the radius of the later is $14$ m, then what is the radius of the former?

  1. $10$ m
  2. $8$ m
  3. $12$ m
  4. $16$ m
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B Correct answer
Explanation

The ratio of the areas of two circles is the square of the ratio of their radii. If the ratio of areas is 16:49, the ratio of radii is sqrt(16):sqrt(49) = 4:7. Given the radius of the later circle is 14 m, we set 7x = 14, so x = 2. The radius of the former is 4 * 2 = 8 m.

AI explanation

The areas of circles are proportional to the squares of their radii, giving the ratio of the radii as the square root of the area ratio, 16 to 49, which is 4 to 7. Let the former radius be 4x and the latter radius be 7x, which we know equals 14 m, so x equals 2 m. The former radius is 4x, which calculates to 8 m.

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