Multiple choice

If the radii of two circles re $7\,cm$ and $24\,cm$, then the radius of the circle having area equal to the sum of the areas of the two circles, is

  1. $31\, cm$
  2. $25\, cm$
  3. $17\, cm$
  4. $28\, cm$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The combined area is pi(7^2) + pi(24^2) = pi(49 + 576) = 625pi. Thus the equivalent radius satisfies r^2 = 625, giving r = 25 cm.

AI explanation

The sum of the areas of the two circles is pi * 7 squared + pi * 24 squared, resulting in 49pi + 576pi = 625pi. Let R be the radius of the new circle, so its area is pi * R squared. Equating the areas gives pi * R squared = 625pi, so R squared = 625 and R = 25 cm.

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