Answer: D. 78.5%
Step-by-step explanation:
In the given figure, we have a square having an inscribed circle.
Then the side length of square = [tex]2\times \text{Radius of circle}[/tex]
Since, the radius of the circle = 8 units
Then, the side length of square = [tex]2\times 8=16\ units[/tex]
Now, the area of square =[tex]side^2=(16)^2=256\ units^2[/tex]
The area of circle =[tex]\pi r^2=(3.14)(8)^2=(3.14)(64)=200.96\ units[/tex]
Now, the probability that the dart hits a point in the circle is given by :-
[tex]\text{P(Dart hit in circle)}=\frac{\text{Area of circle}}{\text{Area of square}}\\\\\Rightarrow\text{P(Dart hit in circle)}=\frac{200.96}{256}=0.785[/tex]
In percent, [tex]\text{P(Dart hit in circle)}=0.785\times100=78.5\%[/tex]
Hence, the probability that the dart hits a point in the circle =78.5%
