Question

the difference between the area of a circle and the square of its radius is 16.8 m2 . find the radius of the circle

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{r}\mathrm{be}\mathrm{the}\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{circle},\mathrm{then} \\ \mathrm{area}\mathrm{of}\mathrm{circle}-{\mathrm{r}}^2=16.8{\mathrm{m}}^2 \\ \Rightarrow {\mathrm{\pi r}}^2-{\mathrm{r}}^2=16.8 \\ \Rightarrow \left(\mathrm{\pi }-1\right){\mathrm{r}}^2=16.8 \\ \Rightarrow \left[\frac{22}{7}-1\right]{\mathrm{r}}^2=16.8 \\ \Rightarrow \frac{15}{7}{\mathrm{r}}^2=16.8 \\ \Rightarrow {\mathrm{r}}^2=7.84 \\ \Rightarrow \mathrm{r}=2.8 \\ \mathrm{So},\mathrm{radius}\mathrm{of}\mathrm{the}\mathrm{circle}=2.8\mathrm{m} \end{gathered}$$