Chapter 11.3, Problem 45HP

To determine

The area of the shaded region.

Answer to Problem 45HP

The area value is $\text{A}\left(\text{shaded}\right)\text{=}449.0{\text{cm}}^2$

Explanation of Solution

Given information:

Find the area of the shaded region. Round to the nearest tenth

  

Formula used:

  $\text{A}\left(\text{shaded}\right)\text{=A}\left(\text{lg}\text{sector}\right)\text{-A}\left(\text{sm}\text{.sector}\right)$

Calculation:

The radius of the larger circle is 17.5 cm and that of the smaller circle is 7 cm. 

The measure of the central angle of the shaded region is 360 − 160 = 200. 

  $\begin{array}{l}\text{A}\left(\text{shaded}\right)\text{=A}\left(\text{lg}\text{sector}\right)\text{-A}\left(\text{sm}\text{.sector}\right)\\ =\frac{200}{360}\pi {\left(17.5\right)}^2-\frac{200}{360}\pi {\left(7\right)}^2\\ =\frac{5}{9}\pi \left(306.25\right)-\frac{5}{9}\pi \left(49\right)\\ =\frac{1531.25-245}{9}\pi \\ \text{A}\left(\text{shaded}\right)\text{=}449.0{\text{cm}}^2\end{array}$

Conclusion:

The area value is $\text{A}\left(\text{shaded}\right)\text{=}449.0{\text{cm}}^2$