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.

Answer 1

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

$$\begin{gathered} \Rightarrow \mathrm{\pi }{r}^2=\mathrm{\pi }{\left(8\right)}^2+\mathrm{\pi }{\left(6\right)}^2 \\ \Rightarrow r^2=64+36 \\ \Rightarrow r^2={10}^2 \\ \Rightarrow r=10\mathrm{cm} \end{gathered}$$
Hence, the radius of the circle is 10 cm.