Answer:
B. about 60%
Step-by-step explanation:
Let us assume that the radius of the semi-circle is d units.
So the area of the semi-circle will be,
[tex]=\dfrac{\pi d^2}{2}[/tex]
In total there are 4 semi circles, so the net area will be,
[tex]=4\times \dfrac{\pi d^2}{2}[/tex]
[tex]=2\pi d^2[/tex]
The side length of the square is twice the radius of the semi circle. So the side length of the square is 2d units.
Area of the square is,
[tex]=(2d)^2\\\\=4d^2[/tex]
The total area will be,
[tex]=2\pi d^2+4d^2[/tex]
So that the random point will be in the shaded region is,
[tex]=\dfrac{\text{Area of semi circles}}{\text{Area of square}}[/tex]
[tex]=\dfrac{2\pi d^2}{2\pi d^2+4d^2}[/tex]
[tex]=\dfrac{2\pi}{2\pi+4}[/tex]
[tex]=0.6[/tex]
[tex]=60\%[/tex]
