Multiple choice

What is the radius of a circle to the nearest cm whose area is equal to the sum of the areas of three circles of radii $22$ cm, $19$ cm and $8 $cm respectively

  1. $17 cm$
  2. $30 cm$
  3. $29 cm$
  4. $19 cm$
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B Correct answer
Explanation

The area of the new circle is the sum of the areas of the three circles: pi * R^2 = pi * (22^2 + 19^2 + 8^2). R^2 = 484 + 361 + 64 = 909. The square root of 909 is approximately 30.15, which rounds to 30 cm.

AI explanation

The area of a circle is found using the formula pi * r^2. The total area is the sum of the areas of the three given circles, calculated as pi * 22^2 + pi * 19^2 + pi * 8^2. This gives a total area of pi * 484 + pi * 361 + pi * 64, which equals 909pi cm^2. Setting this equal to the area of a single circle gives pi * R^2 = 909pi, so R^2 = 909. The square root of 909 is approximately 30.14, which rounds to the nearest centimeter as 30 cm.

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