Question

The blade of a windshield wiper sweeps out an angle of 135° in one cycle. The base of the blade is12 inches from the pivot point and the tip is 32 inches from the pivot point. What area does thewiper cover in one cycle? (Round to the nearest 0.1 square inch.)

Answer 1

The area covered by the windshield wiper in one cycle is approximately 150.8 square inches.

Step-by-step explanation:

To find the area covered by the windshield wiper in one cycle, we need to calculate the area of the sector formed by the angle swept by the wiper. Since the base of the blade is 12 inches from the pivot and the tip is 32 inches from the pivot, the radius of the sector is 32 inches. The formula to calculate the area of a sector is A = (1/2) * r^2 * θ, where r is the radius and θ is the angle in radians.

First, we need to convert the angle from degrees to radians. 135 degrees is equal to 2.356 radians (approximately). Now we can substitute the values into the formula:

A = (1/2) * 32^2 * 2.356 = 150.796 square inches (rounded to the nearest 0.1).

Answer 2

The are cover in one cycle is 1036.7 square inches.

Step-by-step explanation:

Consider the provided information.

The blade of a windshield wiper sweeps out an angle of 135° in one cycle. The base of the blade is12 inches from the pivot point and the tip is 32 inches from the pivot point.

The area of a sector is:
`(1)/(2)r^2\theta` where θ is in radians.

First Converting 135º to radians, we get 3π/4.

The area of the region swept out by the wiper blade = (Area cover by tip) - (area of blade).

`Area = (1)/(2)(32)^2* (3\pi)/(4) -(1)/(2)(12)^2* (3\pi)/(4)\\\\Area = (3\pi)/(8)(32^2 - 12^2) \approx1036.73`

The are cover in one cycle is 1036.7 square inches.