Multiple choice

It is proposed to build a single circular park equal in area to the sum of areas of two circular parks of diameters $16 m$ and $12 m$ in a locality. The radius of the new park could be

  1. $10m$
  2. $15cm$
  3. $20m$
  4. $24cm$
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A Correct answer
Explanation

The area of the new circle is the sum of the areas of the two given circles: pi*R^2 = pi*(d1/2)^2 + pi*(d2/2)^2. Substituting diameters 16m and 12m gives R^2 = 8^2 + 6^2 = 64 + 36 = 100, so R = 10m.

AI explanation

The radii of the two smaller parks are 8 m and 6 m. The area of the new park equals the sum of their areas, so pi multiplied by R squared equals pi multiplied by 8 squared plus pi multiplied by 6 squared. Dividing by pi gives R squared equal to 64 plus 36, which is 100. Therefore, the radius of the new park is 10 m.

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