Given a circle with radius 6 m and centre O. The points 
and 
are drawn on the circle so that the angles 
and 
are right angles (as shown in the diagram below for one of the possible drawn situations). The size of the angle 
depends on the selection of the positions of the points 
and on the circle.
Prove that for any points 
and 
drawn in this way, the area of the shaded area as a function of the size of the angle 
is equal to 
, if the angle 
is expressed in radians.
For which obtuse angle is the area of the shaded area the largest? Round the angle to the nearest tenth of a degree.
The diagram above also shows the cross-section of a tunnel with a plane perpendicular to the direction of travel. The circle has a radius of 
, the width of the tunnel is 
, and its length is 
. The curved ceiling and walls of the tunnel will be painted over. For this purpose, 400 l of paint was bought. Will there be enough paint if they use exactly 5 l of paint for 
? Justify your answer.
paint for 
area, so we don't have enough.
