The arm and blade of a windshield wiper have a total length

The arm and blade of a windshield wiper have a total length of 30 inches of the blade is 24 inches long and the wiper sweeps out an angle of 125 degree, how much window area can the blade clean? An object is traveling on a circle of radius 5 m. If in 20 seconds the object travels 5 meters, what is its angular speed and its linear speed? A DVD drive has a maximum speed of 7200 revolutions over minute (rpm). If a DVD diameter is 12 cm. What is the linear speed, in km/h, of a point 5 cm from the disc\'s center if it is spinning at 5400 rpm? Charleston, West Virginia is due north of Jacksonville, FL. Charleston is located at 38 degree 21\' north latitude and Jacksonville is located at 30 degree 20\' north latitude. The radius of the earth is 3960 miles. Find the distance between Charleston and Jacksonville.

Solution

1)
First we need to figure out what\'s left when we subtract a smaller circle (arm) from a bigger circle (arm + blade):
Area is given by pi*r^2
Total length=30in
blade length=24in
so, arm length=30-24=6in
30^2 pi is the whole circle if arm were part of the blade.
6^2 pi is the part covered by the arm.
So we start with Area the blade can clean= total area-area of arm=30^2 pi - 6^2 pi = 864 pi.
Now,
Area is given by= (125/360 degrees) (pi x r squared)
Then multiply that by 125/360
So,
Area=125/360*864 pi=942.47 sq in