automobiles suppose the arm of a windshield wiper is 16 in. long, with a blade 12 in. long. if the wiper moves through an angle of 90degree, how much of the windshield is cleaned in one pass of the wiper ?

sketch a quarter circle with an outer radius of 16

and an inner radius of 4
So the area not wiped has to be subtracted form the area of the whole quarter circle, so ...

find the area of 1/4 circle with radius 16
find the area of 1/4 circle with radius 4
subtract and you are done.

To calculate how much of the windshield is cleaned in one pass of the wiper, we need to find the length of the arc described by the wiper blade.

The length of an arc can be calculated using the formula:
Arc Length = (θ/360) * 2πr

Where:
- θ is the angle in degrees
- r is the radius of the circle formed by the wiper arm

In this case, the angle is given as 90 degrees, and the wiper arm length is 16 inches. However, we need to find the radius of the circle formed by the wiper arm.

To find the radius, we can use the Pythagorean theorem:
r² = arm length² - blade length²

Substituting the given values:
r² = 16² - 12²
r² = 256 - 144
r² = 112
r ≈ √112
r ≈ 10.58 inches

Now we can calculate the arc length using the formula:
Arc Length = (90/360) * 2π * 10.58

Arc Length = (1/4) * 2 * 3.14 * 10.58
Arc Length ≈ 0.785 * 6.28 * 10.58
Arc Length ≈ 15.71 inches

Therefore, in one pass of the wiper, approximately 15.71 inches of the windshield is cleaned.