Respuesta :
Answer:
63.7%
Explanation:
To know the probability, we need to calculate the area of the circle and the area of the square.
The area of the circle is equal to:
[tex]A_c=\pi\cdot r^2[/tex]Where r is the radius of the circle and π is approximately 3.14. So, the area of the circle is:
[tex]\begin{gathered} A_c=3.14\times4^2 \\ A_c=3.14\times16 \\ A_c=50.24 \end{gathered}[/tex]On the other hand, the area of the square is equal to:
[tex]\begin{gathered} A_s=\text{Base}\times Height \\ A_s=4\sqrt[]{2}\times4\sqrt[]{2} \\ A_s=32 \end{gathered}[/tex]Now, the probability that a randomly selected point within the circle falls in the square area is equal to the ratio of the areas calculated above. So, the probability is:
[tex]P=\frac{A_s}{A_c}=\frac{32}{50.24}=0.637=63.7\text{ \%}[/tex]Therefore, the answer is 63.7%
