1 Answer

Yogesh Badke · Answer 1 · 2023-10-16T14:04:22+0000

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;

$18.7\text{ }in^2$

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