Question

Both circles have the same center. What is the area of the shaded region?

Answer 1

Notice, the diameter for the smaller circle  is 19.2, thus its radius is half that, or 9.6.

the radius from the center to the outer circle is then 9.6 + 18.1.

$\bf \textit{area of a circular ring}\\\\ A=\pi (R^2-r^2)~~ \begin{cases} R=\textit{radius from center}\\ \qquad \textit{to outer circle}\\ r=\textit{radius from center}\\ \qquad \textit{to inner circle}\\ ----------\\ r=\frac{19.2}{2}\\ \qquad 9.6\\\\ R=\frac{19.2}{2}+18.1\\ \qquad 9.6+18.1\\ \qquad 27.7 \end{cases} \\\\\\ A=\pi (27.7^2-9.6^2)$