Question

Find the area of the shaded region in the figure Type an integer or decimal rounded to the nearest TENTH

Answer 1

The area of the shaded region is;

`18.7\text{ }in^2`

Step-by-step explanation:

Given the figure in the attached image.

The area of the shaded region is the area of the larger circle minus the area of the smaller circle;

`\begin{gathered} A=(\pi D^2)/(4)-(\pi d^2)/(4) \\ A=(\pi)/(4)(D^2-d^2) \end{gathered}`

Given;

`\begin{gathered} D=6 \\ d=3(1)/(2) \end{gathered}`

Substituting the given values;

`\begin{gathered} A=(\pi)/(4)(D^2-d^2) \\ A=(\pi)/(4)(6^2-3.5^2) \\ A=(\pi)/(4)(23.75) \\ A=18.65\text{ }in^2 \\ A=18.7\text{ }in^2 \end{gathered}`

Therefore, the area of the shaded region is;

`18.7\text{ }in^2`