Multiple choice

The diameter of a circle whose area is equal to the sum of the area of two circles of diameter $16 cm$ and $12 cm$ is:

  1. $56 cm$
  2. $42 cm$
  3. $28 cm$
  4. $20 cm$
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D 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 = 10. Diameter = 2 * R = 20 cm.

AI explanation

The new circle's area equals the sum of the areas of the two given circles, written as pi times R squared equals pi times 8 squared plus pi times 6 squared. Dividing by pi gives R squared equals 64 plus 36, which equals 100. The radius R is 10 cm, making the diameter 20 cm.

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