Question

Jeremy plants flowers in a circular bed with a diameter of 3, represented by the unshaded circle in the diagram. He builds a circular patio around the flowers with a diameter of 8, represented by the shaded portion of the diagram. Both circles share the same center. What is the area of the patio? Use 3.14 for \pi.

Answer 1

`\textit{Area of a circular ring}\\\\ A=\pi (R^2 - r^2) ~~ \begin{cases} R=\stackrel{large}{radius}\\ r=\stackrel{small}{radius}\\[-0.5em] \hrulefill\\ R=8\\ r=3 \end{cases}\implies A=\pi (8^2 - 3^2) \\\\\\ A=55\pi \implies A=55(3.14)\implies A=172.7~cm^2`