The windshield wiper on the driver's side of a large bus is depicted below. Arm AB pivots back and forth around point A, sweeping out an arc of 60∘, symmetric about the vertical line through A. The wiper blade CD is attached to B at its midpoint and stays vertical as the arm moves. The arm is 3 feet long, and the wiper blade is 3.5 feet tall. What is the area of the windshield cleaned by the wiper, in square feet, to the nearest hundredth? (Assume that the windshield is a flat vertical surface.)
(A)9.68(B)10.14(C)10.50(D)11.32(E)12.00
AO2=AO1=BC=BD=B′C′=B′D′=23.5=1.75 C goes to C′ with center O2.
D goes to D′ with center O1.
A1:Area of Circular Segment CC′MA2:Area of Circular Segment DD′NA1=A2⇒Areashaded=Areashaded−A1+A2=[CC′D′D]=CD⋅DD′=3.5DD′
△DD′O1 is an equilateral triangle⇒DD′=3 By Hint 4,Ans=3.5(3)=10.5
