Find the area.

Question

A car’s rear windshield wiper rotates 125 degrees.
The total length of the wiper mechanism is 25 inches
and wipes the windshield over a distance of 14 inches.
Find the area covered by the wiper.

Answer 1

Step 1:

The total length of the wiper mechanism is inches.

The distance moved by wiper is inches.

Arc radius

A car’s rear windshield wiper rotates .

Convert degrees into radians.

Step 2:

The area of sector of a circle 

Area of the sector is

The area of the sector with radius is

Step 3:

Area covered by the wiper = Area of the sector - The area of the sector with radius .

Area covered by the wiper = .

Area covered by the wiper =  sq-inches.

Solution:

Area covered by the wiper is sq-inches.