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,
\(=\dfrac{\pi d^2}{2}\)
In total there are 4 semi circles, so the net area will be,
\(=4\times \dfrac{\pi d^2}{2}\)
\(=2\pi d^2\)
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,
\(=(2d)^2\\\\=4d^2\)
The total area will be,
\(=2\pi d^2+4d^2\)
So that the random point will be in the shaded region is,
\(=\dfrac{\text{Area of semi circles}}{\text{Area of square}}\)
\(=\dfrac{2\pi d^2}{2\pi d^2+4d^2}\)
\(=\dfrac{2\pi}{2\pi+4}\)
\(=0.6\)
\(=60\%\)
