Question:
The radii of two circles are 8 cm and 6 cm. Find the radius of the circle having area equal to the sum of the areas of the two circles.
Solution:
Let the radius of the required circle be r.
Now, Area of the required circle = Area of circle having radius 8 cm + Area of circle having radius 6 cm
$\Rightarrow \pi r^{2}=\pi(8)^{2}+\pi(6)^{2}$
$\Rightarrow r^{2}=64+36$
$\Rightarrow r^{2}=10^{2}$
$\Rightarrow r=10 \mathrm{~cm}$
Hence, the radius of the circle is 10 cm.
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