Multiple choice

What is the radius of the circle whose area is equal to the sum of the areas of two circles whose radii are 15 cm and 8 cm?

  1. 14 cm

  2. 13 cm

  3. 15 cm

  4. 17 cm
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D Correct answer
Explanation

Area = pi*r^2. Sum of areas = pi*(15^2) + pi*(8^2) = pi*(225 + 64) = 289*pi. New radius r satisfies pi*r^2 = 289*pi, so r^2 = 289, r = 17.

AI explanation

Using the area addition formula for circles, the area of the new circle equals the sum of the areas of the two given circles: πR² = πr₁² + πr₂². By factoring out π, this simplifies to R² = 15² + 8² = 225 + 64 = 289. Taking the positive square root gives a radius of R = 17 cm.

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