Question

The difference between the area of a circle and the square of its radius is $16.8{\mathrm{m}}^2$. Find the radius of the circle.

Answer 1

Determine the radius of the circle.

The area of the circle $\left(A_1\right)$ is calculated by $A_1={\mathrm{\pi r}}^2$ where $r$ represents the radius of the circle.

The area of square $\left(A_2\right)$ is calculated by $A_2=s^2$ where $s$ represents the side of the square.

It is given that the radius of circle $\left(r\right)$ is equal to the side of the square $\left(s\right)$.

The difference between the area of a circle and the square of its radius is $16.8{\mathrm{m}}^2$.

$$\begin{gathered} \Rightarrow A_1-A_2=16.8 \\ \Rightarrow {\mathrm{\pi r}}^2-{\mathrm{s}}^2=16.8 \\ \Rightarrow {\mathrm{\pi r}}^2-{\mathrm{r}}^2=16.8\left[r=s\right] \\ \Rightarrow \mathrm{r}=\sqrt{\frac{16.8}{\mathrm{\pi }-1}}[\mathrm{Radius}\mathrm{cannot}\mathrm{be}\mathrm{negative}] \\ =\sqrt{\frac{16.8}{3.14-1}} \\ =2.8\mathrm{m} \end{gathered}$$

Hence, the radius of the circle is $2.8\mathrm{m}$.