Multiple choice

The diameters of two circles are $32:cm$ and $24: cm$ . Find the radius of the circle having its area equal to sum of the areas of the two given circle.

  1. $20 \: cm$
  2. $41\: cm$
  3. $52 \: cm$
  4. $62 \: cm$
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A Correct answer
Explanation

Radii are 16 and 12. Areas are pi * 16^2 and pi * 12^2. Sum = pi * (256 + 144) = pi * 400. New radius^2 = 400, so radius = 20.

AI explanation

The areas of the two circles are pi times 16 squared and pi times 12 squared, totaling pi times 400 square cm. Equating this to the new circle area, pi times R squared equals pi times 400, meaning R equals 20 cm.

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