Multiple choice

The radius of a circle whose area is equal to the sum of the ares of two circles of radii 3 cm and 4 cm is

  1. 5 cm

  2. 5.5 cm

  3. 5.8 cm

  4. 6 cm
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A Correct answer
Explanation

Area of circle 1 = pi * 3^2 = 9pi. Area of circle 2 = pi * 4^2 = 16pi. Sum = 25pi. The new circle has area pi * R^2 = 25pi, so R = 5.

AI explanation

The sum of the areas of the two circles is 3 squared pi plus 4 squared pi, which equals 9 pi plus 16 pi, or 25 pi. Since this sum equals the area of the third circle, pi times the new radius squared equals 25 pi. Dividing by pi and taking the square root gives the radius as 5 cm.

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