Given: an image containing a square and an inscribed circle as shown
To Determine: The probability of hitting the shaded area
Solution
The area of a circle and a rectangle can be calculated using the formula
[tex]\begin{gathered} Area(circle)=\pi r^2 \\ Area(square)=l^2 \end{gathered}[/tex]
From the image we can observed that
Let us substitute the radius and the side length to get the areas as shown below
[tex]\begin{gathered} Area(circle)=\pi(8)^2=64\pi-square-units \\ =201.0619-square-units \end{gathered}[/tex][tex]Area(square)=16^2=256-square-units[/tex]
The area of the shaded area is
[tex]\begin{gathered} Area(shaded)=Area(square)-Area(circle) \\ Area(shaded)=256-201.0619=54.9381-square-units \end{gathered}[/tex]
The probability of hitting the shaded area in each problem would be
[tex]\begin{gathered} P(Shaded)=\frac{Area(shaded)}{Area(square)} \\ P(shaded)=\frac{54.9381}{256}=0.2146 \\ P(shaded)-as-percent=0.2146\times100\%=21.46\%\approx21.5\% \end{gathered}[/tex]
Hence, the probability of hitting the shaded area to the nearest tenth is 21.5%
