Question

The radius of a circle is 14 cm. Find the radius of the circle whose area is double of the area of the circle.

Answer 1

Let the area of the circle whose radius is 14 cm be A_1.
Let the radius and area of the circle, whose area is twice the area of the circle A_{1 ,} be r₂ and A₂, respectively.

Thus,
A₁ = $\mathrm{\pi }{\left(\mathrm{r}\right)}^2=\mathrm{\pi }{\left(14\right)}^2=\left(\frac{22}{7}\times 14\times 14\right){\mathrm{cm}}^2=\left(44\times 14\right){\mathrm{cm}}^2=616{\mathrm{cm}}^2$.
A₂ = 2 $\times$ A₁ = 2 $\times$ 616 = 1232 cm²
A₂ = $\mathrm{\pi }{\left({\mathrm{r}}_2\right)}^2$ = 1232 cm^{2
$$\begin{gathered} \Rightarrow \left(\frac{22}{7}\times {r_2}^2\right)=1232{\mathrm{cm}}^2 \\ \Rightarrow {r_2}^2=\frac{1232\times 7}{22}=(56\times 7){\mathrm{cm}}^2 \\ \Rightarrow r_2=\sqrt{56\times 7}=\sqrt{7\times 8\times 7}=\sqrt{7\times 7\times 4\times 2}=14\sqrt{2}\mathrm{cm} \end{gathered}$$}

Hence, the radius of the circle A₂ is 14$\sqrt{2}$ cm.