Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Area of red zone is $\frac{17}{4}\pi {{\text{m}}^{2}}$
Compare the outer and inner circle equation with the standard equation of a circle. ${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$ For outer circle radius it would be ${{r}_{o}}^{2}=\frac{81}{4}$. And for the inner circle it would be ${{r}_{i}}^{2}=16$ Use the formula for Area of a circle to calculate the red zone area, $A=\pi {{r}^{2}}$. The area of red zone is the difference between the area of outer and inner circles. Put the value of outer and inner radius in the formula, $A=\pi {{r}^{2}}$ \begin{align} & \text{Area of red zone}=\pi {{r}_{o}}^{2}-\pi {{r}_{i}}^{2} \\ & =\left( \pi \times \frac{81}{4} \right)-\left( \pi \times 16 \right) \\ & =\pi \left( \frac{81-64}{4} \right) \\ & =\frac{17}{4}\pi {{\text{m}}^{2}} \end{align} Thus, the area of red zone is $\frac{17}{4}\pi {{\text{m}}^{2}}$.