Question

Find the area enclosed between two concentric circles of radii 3.5 cm and 7 cm. A third concentric circle is drawn outside the 7 cm circle , such that the area enclosed between it and the 7 cm circle is same as that between the two inner circles . Find the radius of the third circle correct to one decimal place.

Answer 1

The area enclosed between the two circles of radii 3.5 cm and 7 cm
$$\begin{gathered} =\mathrm{\pi }\left(7^2-3.5^2\right) \\ =115.5{\mathrm{cm}}^2 \end{gathered}$$
Let the radius of the outermost circle be r cm.
Area betweent the circles with radius r and 7 cm=Area between the circles with radius 7 cm and 3.5 cm
$$\begin{gathered} \mathrm{\pi }\left({\mathrm{r}}^2-7^2\right)=115.5 \\ \Rightarrow \left({\mathrm{r}}^2-7^2\right)=\frac{115.5}{\mathrm{\pi }} \\ \Rightarrow {\mathrm{r}}^2=36.75+49=85.75{\mathrm{cm}}^2 \\ \Rightarrow \mathrm{r}=9.26\mathrm{cm} \end{gathered}$$