Question

If $A=\pi r^2$, solve $r$, and find the value of '$r$' if $A=77$ and $\pi =\frac{22}{7}$.

Answer 1

The given quadratic equation $A=\pi r^2$ is the area of the circle with radius $r$.

Substitute $A=77$ and $\pi =\frac{22}{7}$ in the equation $A=\pi r^2$ as follows:

$A=\pi r^2\Rightarrow 77=\frac{22}{7}{r}^2\Rightarrow 77\times 7=22r^2\Rightarrow 22r^2=539\Rightarrow r^2=\frac{539}{22}\Rightarrow r^2=\frac{49}{2}\Rightarrow r=\sqrt{\frac{49}{2}}\Rightarrow r=\pm \frac{7}{\sqrt{2}}$

Since radius cannot be negative, therefore, $r=\frac{7}{\sqrt{2}}$

Hence, $r=\frac{7}{\sqrt{2}}$.