Question

The radius of one circular field is 5 m and that of the other is 13 m. Find the radius of the circular field whose area is the difference of the areas of first and second field.

Answer 1

Let the area of the circular field whose radius is 5 m be A₁ , and the area of the circular field whose radius is 13 m be A₂. Let A₃ and r cm be the area and radius of the circular field, that is equal to the difference of the areas of the two fields.
∴ A₃ = A₂ - A₁

$$\begin{gathered} A_1=\mathrm{\pi }{\left(5\right)}^2=\left(25\mathrm{\pi }\right){\mathrm{m}}^2 \\ {A}_2=\mathrm{\pi }(13{)}^2=\left(169\mathrm{\pi }\right){\mathrm{m}}^2 \\ {A}_3=A_2-A_1=\left(169\mathrm{\pi }\right)-\left(25\mathrm{\pi }\right)=144\mathrm{\pi }{\mathrm{m}}^2 \\ \Rightarrow A_{\mathit{3}}=\mathrm{\pi }{\left(r\right)}^2=144\mathrm{\pi }{\mathrm{m}}^2 \\ \Rightarrow {\left(r\right)}^2=144{\mathrm{m}}^2 \\ \Rightarrow r=\sqrt{144}\mathrm{m}=12\mathrm{m} \end{gathered}$$

Hence, the radius of the circular field is 12 m.