Question

find the area of the shaded region in the figure. use the (pi) key for (pi). the area of the shaded region in the figure is approximately (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Recall area - of - circle formula

The area of a circle is given by $A = \pi r^{2}$, where $r$ is the radius of the circle. Let the outer - radius be $R$ and the inner - radius be $r$.

Step2: Identify outer and inner radii

The outer diameter is $10$ inches, so the outer radius $R=\frac{10}{2}=5$ inches. The inner diameter is $8\frac{1}{2}$ inches, so the inner radius $r = \frac{8.5}{2}=4.25$ inches.

Step3: Calculate area of outer circle

$A_{outer}=\pi R^{2}=\pi\times(5)^{2}=25\pi$ square inches.

Step4: Calculate area of inner circle

$A_{inner}=\pi r^{2}=\pi\times(4.25)^{2}=18.0625\pi$ square inches.

Step5: Calculate area of shaded region

The area of the shaded region $A = A_{outer}-A_{inner}=\pi(25 - 18.0625)=6.9375\pi$ square inches.
Using $\pi\approx3.14$, we have $A\approx6.9375\times3.14 = 21.8$.

Answer:

$21.8$