Question

Find the probability of hitting the shaded area in each problem. Round your answers to the nearest tenth.

Answer 1

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

`\begin{gathered} Area(circle)=\pi r^2 \\ Area(square)=l^2 \end{gathered}`

From the image we can observed that

Let us substitute the radius and the side length to get the areas as shown below

`\begin{gathered} Area(circle)=\pi(8)^2=64\pi-square-units \\ =201.0619-square-units \end{gathered}`
`Area(square)=16^2=256-square-units`

The area of the shaded area is

`\begin{gathered} Area(shaded)=Area(square)-Area(circle) \\ Area(shaded)=256-201.0619=54.9381-square-units \end{gathered}`

The probability of hitting the shaded area in each problem would be

`\begin{gathered} P(Shaded)=(Area(shaded))/(Area(square)) \\ P(shaded)=(54.9381)/(256)=0.2146 \\ P(shaded)-as-percent=0.2146*100\%=21.46\%\approx21.5\% \end{gathered}`

Hence, the probability of hitting the shaded area to the nearest tenth is 21.5%