Question

Radii of two circles are 3 m and 4 m respectively. Find the radius of a circle having area equal to the sum of the areas of these two circles

Answer 1

We know the area of a circle $=\pi r^2$

Hence, area of a circle$\left(C_1\right)$ of radius $3m=\frac{22}{7}\times {\left(3\right)}^2$

Area of a circle$\left(C_2\right)$ of radius $4m=\frac{22}{7}\times {\left(4\right)}^2$

Given, area of big circle $=$ sum of the areas of circles $C_1$ and $C_2$

$=\frac{22}{7}\times 3^2+\frac{22}{7}\times 4^2$

$=\frac{22}{7}\times (9+16)$

$=\frac{22}{7}\times \left(25\right)$

Let the radius of the big circle be $R.$

Area of big circle $=\pi R^2=\frac{22}{7}\times \left(25\right)$

$\Rightarrow R^2=25$

$\Rightarrow R=5m$