Acar's rear windshield wiper rotates 140°. the total length of the wiper mechanism is 24 inches and the length of the wiper blade is 13 inches. find the area wiped by the wiper blade.

The area wiped by the wiper blade is

Step-by-step explanation:

Given:

car's rear windshield wiper rotates  =  140°

Total length of the wiper mechanism =  24 inches

Length of the wiper blade = 13 inches

To Find:

The area wiped by the wiper blade = ?

Solution:

The length of the wiper mechanism , = 24

The length of the wiper mechanism ,  = 13

Now arc radius

= 24-13 = 11

The wipe rotates 140 degrees

Step 1: converting degree into radians

Step 2: Finding the area of the sector of the circle with radius

The area of the sector  

=

=

=

= ---------------------------(1)

Step 2: Finding the area of the sector with radius

=

=

=

= ---------------------------(2)

Step 3: Finding the area  wiped by the wiper

The area  wiped by the wiper =  the area of the sector of the circle with radius  -  the area of the sector with radius

From(1) and(2)

The area  wiped by the wiper = -  

The area  wiped by the wiper =  

The area  wiped by the wiper =  

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