8 A circle, centre \(O\), has radius \(x \mathrm {~cm}\), where \(x\) is an observation from the random variable \(X\) which has a rectangular distribution on \([ 0 , \pi ]\)
- Find the probability that the area of the circle is greater than \(10 \mathrm {~cm} ^ { 2 }\)
- State, giving a reason, whether the median area of the circle is greater or less than \(10 \mathrm {~cm} ^ { 2 }\)
The triangle \(O A B\) is drawn inside the circle with \(O A\) and \(O B\) as radii of length \(x \mathrm {~cm}\) and angle \(A O B x\) radians.
- Use algebraic integration to find the expected value of the area of triangle \(O A B\). Give your answer as an exact value.