Question

Find the probability that a randomlyselected point within the circle fallsin the red shaded area (square).r= 4 cm412 cm[? ]%Round to the nearest tenth of a percent.Enter

Answer 1

63.7%

Step-by-step 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:

`A_c=\pi\cdot r^2`

Where r is the radius of the circle and π is approximately 3.14. So, the area of the circle is:

`\begin{gathered} A_c=3.14*4^2 \\ A_c=3.14*16 \\ A_c=50.24 \end{gathered}`

On the other hand, the area of the square is equal to:

`\begin{gathered} A_s=\text{Base}* Height \\ A_s=4\sqrt[]{2}*4\sqrt[]{2} \\ A_s=32 \end{gathered}`

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:

`P=(A_s)/(A_c)=(32)/(50.24)=0.637=63.7\text{ \%}`

Therefore, the answer is 63.7%