Chapter 11.6, Problem 15PSB

To determine

To calculate: Thearea of shaded regionwhich contain one larger circle and three identical smaller circles.

Answer to Problem 15PSB

The area of shaded region is $12\pi$ .

Explanation of Solution

Given information:

Three smaller circles are of radius 2 and larger circle is of radius 6.

Formula used:

Area of a circle: $A=\pi r^2$

r = radius of a circle.

  $A_{shadedarea}=A_{largercircle}-3A_{smallercircle}$

Calculation:

  

  $\begin{array}{l}{A}_{largercircle}=\pi r^2\\ $ =\pi {(6)}^2$=36\pi \\ A_{smallercircle}=\pi r^2\\ $ =\pi {(2)}^2$=4\pi \\ A_{shadedarea}=\frac{1}{2}{A}_{outercircle}-(3\ast \frac{1}{2}{A}_{innercircle})\\ A_{shadedarea}=\frac{1}{2}\ast 36\pi -\frac{3}{2}\ast 4\pi \\ A_{shadedarea}=18\pi -6\pi \\ A_{shadedarea}=12\pi \end{array}$