Multiple choice

The radius of a circle whose area is equal to the sum of the areas of two circles of radii 5 cm and 12 cm is

  1. 13 cm

  2. 14 cm

  3. 15 cm

  4. 17 cm
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A Correct answer
Explanation

Area of circle = pi * r^2. Sum of areas = pi * 5^2 + pi * 12^2 = pi * (25 + 144) = pi * 169. Since pi * R^2 = pi * 169, R^2 = 169, so R = 13.

AI explanation

The area of a circle with radius 5 is 25 pi and the area of a circle with radius 12 is 144 pi, making the sum of their areas 169 pi. The area of the new circle equals this sum, so pi times the new radius squared equals 169 pi. Dividing by pi and taking the square root gives the radius as 13 cm.

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