Answer:
0.36
Step-by-step explanation:
Given, a circle with radius, [tex]r=4 \ cm[/tex]
Area of circle =[tex]\pi r^2[/tex]
Substitute [tex]r=4[/tex]
Area of whole circle[tex]=\pi r^2\\=\pi\times 4^2\\=16\pi \\=50.2654\ cm^2[/tex]
Square is inscribed in it whose each side is [tex]4\sqrt{2}\ cm[/tex]
Area of square [tex]=side^2\\=(4\sqrt{2} )^2\\=16\times 2\\=32 \ cm^2[/tex]
We can see that area of the white circle
= area of the whole circle - area of square
[tex]=50.2654-32\\=18.2654 \ cm^2[/tex]
Probability of falling a random point within the white circle
[tex]=\frac{area\ of\ white\ circle}{area\ of\ whole\ circle}[/tex]
[tex]=\frac{18.2654}{50.2654} \\=0.3633[/tex]
Rounding to nearest hundredth.
Probability of falling a random point within the white circle would be 0.36