Find the equation of the line the smaller circle with the dot makes - shown as a red line on the animated diagram.
Using my integration thing - I know that the small circle will turn 360 degrees 16 times before it goes around the whole of the bigger circle, so if I put the red lines on to a graph (all 16 of them), with the corresponding portion of the bigger circle circumference (I think it will be
2 x pi units long), and then integrate to find the area below the red line, and then to find the area below the circle line, and take the circle area from the red line area (either do this sixteen times, or once and multiply the answer by sixteen), and then add in the full area of the circle.
The only work I'll need to do is work out the equations of each line... which I can probably do if I can somehow draw a accurate graph.
Similar Threads
Threaded Mode