Question

The sum of the areas of two circles is 770 sq . cm and radius of one of them is 14 cm. Find the radius of other circle.

Answer 1

Radius of first circle be = 14 cm (given)
Let radius of second circle be r₂.
Area of the circle = $\mathrm{\pi }$r^₂

Now, sum of areas of the two circle = Area of first circle +Area of second circle
$\Rightarrow 770=\mathrm{\pi }.{14}^2+\mathrm{\pi }{r_{\mathit{2}}}^2$
$\Rightarrow$ 770 = $\pi$ (14² + r₂²)
$$\begin{gathered} \Rightarrow \frac{770\times 7}{22}=196+{r_2}^2 \\ \Rightarrow 245-196={r_2}^2 \\ \Rightarrow r_2=7\mathrm{cm} \end{gathered}$$

Hence, the radius of second circle is 7 cm.