Chapter 3.3, Problem 11PSA

To determine

To show the area of shared region is of a certain value.

Answer to Problem 11PSA

  $Theareaofashadedregionis100-25\pi .$

Explanation of Solution

Given information:

  $\begin{array}{l}Theradiusoftheinscribedcircleis5,thediameteris10.\\ Thusthesideofthesquareisalso10.\end{array}$

Formula used:

  $\begin{array}{l}Areaofcircle,A=\pi r^2.\\ Areaofsquare,A=s^2.\end{array}$

Calculation:

  $\begin{array}{l}Areaofcircle=\pi r^2\\ =\pi *{\left(5\right)}^2\\ =25\pi \\ Areaofsquare=S^2\\ $ ={(10)}^2$=100\end{array}$

  

  $\begin{array}{l}Thesharedareaistheamountremainingaftersubtractingareaofsquarefromareaof\\ circle:100–25\pi \end{array}$