Chapter 11.6, Problem 24WE

To determine

To Find: The area of region inside both the circles.

Answer to Problem 24WE

  $A=32\pi -64c{m}^2$

Explanation of Solution

Given: $ABCD$ is a square with sides $8cm$ long. Two circles each with radius $8cm$ are drawn one with center $A$ and other with center $C$ .

  

Here

  $s=8$

Area of square.

  $\begin{array}{l}$ A={(s)}^2$$ A={(8)}^2$A=64c{m}^2\end{array}$

Now area of circle inside the circles.

  $\begin{array}{l}A=\pi r^2\\ A=32\pi \end{array}$

Now

Area of region inside both the circles= area of two quarter circles-area of square.

i.e.

  $\begin{array}{l}A=32\pi -64\\ A=32\pi -64c{m}^2\end{array}$