Chapter 11.6, Problem 28WE

To determine

To determine the area of the region enclosed by three circles.

Answer to Problem 28WE

Area between circles is $5.83$ .

Explanation of Solution

Given information :

The radius of the circles are 6 .

  

Area of the equilateral triangle formed of length 12 cm is,

  $A_t=\frac{\sqrt{3}}{4}{\left(12\right)}^2=62.35$

Area of all the three sectors of a triangle with ${60}^{\circ }$ shall be,

  $\begin{array}{l}{A}_s=3\left(\frac{{60}^{\circ }}{{360}^{\circ }}\right)\pi {\left(6\right)}^2\\ A_s=56.52\end{array}$

Hence area between circles is $62.35-56.52=5.83$ .