205k views
5 votes
Find the area of the shaded region in the figure Type an integer or decimal rounded to the nearest TENTH

Find the area of the shaded region in the figure Type an integer or decimal rounded-example-1
User Harlow
by
6.4k points

1 Answer

4 votes

Answer:

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

User Yogesh Badke
by
7.1k points