Multiple choice

The radii of two circles are 6 cm and 8 cm. Find the radius of the circle with area equal to the sum of the areas of these circles.

  1. 20 cm

  2. 5 cm

  3. 2 cm

  4. 10 cm
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D Correct answer
Explanation

Area of circle with radius 6 cm =  $\pi$(6)2 = 36$\pi$ cm2. Area of circle with radius 8 cm = $\pi$ (8)2 = 64$\pi$ cm2.  Total area of both circles = 36$\pi$ cm2 + 64$\pi$cm2 = 100$\pi$ cm2.  So, the radius of the new circle be R. $\pi$R2 = 100$\pi$cm2 R2 = 100 cm2 = R $\Rightarrow$ 10 cm. 

AI explanation

The area of a circle is πr², so the combined area of the two circles is π(6²) + π(8²) = π(36+64) = π(100). For a single circle with this same area, r² must equal 100, so r = 10 cm. This uses the fact that areas of circles of different radii add directly when radius, not diameter, is combined via r².

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