Question

A point in the figure is selected at random. Find the probability that the point will be in the shaded region.


about 80%
about 90%
about 60%
about 70%

Answer 1

Do you have ideas? It is almost the same as your last question.

Answer 2

You have 2 half circles, which is the same size. So together that would be a whole circle. Now you can calculate the circles area, and the square's area.
\[A_{circle}=\pi*r^2\]
\[A_{square}=a*a\]
In this case, \[a=2r\]

Answer 3

So, lets take it in small steps. First try and calculate the circles Area (A). You can use a number if you'd like. This could be \[a=2\] which gives \[r=1\]

Answer 4

\[A_{circle}=\pi*r^2=\pi*1^2=\pi\]
\[A_{square}=a*a=2*2=4\]

Answer 5

\[\frac{A_{circle}}{A_{square}}*100=\frac{\pi}{4}*100 \approx78.5 \]