Question

The radii of two circles are $8cm$ and $6cm,$ respectively$.$ Find the radius of the circle having area equal to the sum of the areas of the two circles.

Answer 1

Area of circle:

It is given that$,$

The radii of the two circles are $8cm$ and $6cm,$

We have to find out the radius of the circle having an area equal to the sum of the areas of the two circles.

Radius $\left(r_1\right)=8cm$

Radius $\left(r_2\right)=6cm$

Area of circle is $=\pi r^{2}c{m}^2$

Area of first circle$$\begin{gathered} =\pi {\left(8\right)}^2 \\ =64\pi c{m}^2 \end{gathered}$$

Area of second circle$$\begin{gathered} =\pi {\left(6\right)}^2 \\ =36\pi c{m}^2 \end{gathered}$$

Total Area $$\begin{gathered} =64\pi +36\pi \\ =100\pi c{m}^2 \end{gathered}$$

Now, assume that the radius of third circle$=R$

Area of the circle third circle $=\pi R^2$

$100\pi =\pi R^2$

$R=10cm.$

Hence, the radius of the circle having an area equal to the sum of the areas of the two circles is $10cm.$