Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
A windscreen wiper turns about a pivot. Its blade covers the points from to away from the pivot. The wiper sweeps an angle of . Find the area of the glass that the blade cleans. Take .
A sector with angle has area . The minor and the major sector add up to the whole circle. A blade between radii and sweeps .
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Plan. Cleaned area the big sector (radius ) minus the small sector (radius ).
Step 1. The big sector. .
Step 2. The small sector. .
Step 3. The difference. .
Answer: .
Check. The shortcut: .
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