Multiple choice

The radius of the circle whose area is equal to the sum of the area of the circles with radius $8$ cm and $6$ cm respectively is

  1. $10$ cm
  2. $9$ cm
  3. $5$ cm

  4. none of these
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A Correct answer
Explanation

Area of circle 1 = pi * 8^2 = 64pi. Area of circle 2 = pi * 6^2 = 36pi. Sum of areas = 100pi. New circle area = pi * R^2 = 100pi, so R^2 = 100, R = 10.

AI explanation

The area of the new circle equals the sum of the areas of the two given circles, so pi * R^2 = pi * 8^2 + pi * 6^2. This simplifies to R^2 = 64 + 36 = 100. Taking the positive square root gives R = 10 cm. The result is 10 cm.

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