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Chapter 4: Problem 118

A car's rear windshield wiper rotates \(125^{\circ} .\) 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.

Short Answer

Expert verified
The area covered by the windshield wiper is obtained by solving the equation from Step 3.

Step by step solution

01

Calculate the Radius

First, calculate the radius of the circle. We are given that the wiper wipes a length of 14 inches, and this is equal to half the circumference of the circle. Using the formula for the circumference of a circle C = 2蟺r, we can solve for the radius r. Set 2蟺r = 14 and solve for r.
02

Calculate the Area

Next, calculate the area of the sector the wiper covers. We are given that the angle the wiper covers is 125 degrees. The formula for the area of a sector of a circle is A = (胃/360) * 蟺 * r虏, where 胃 is the angle in degrees. Plug in the values we know: A = (125/360) * 蟺 * r虏.
03

Solve for the Area

After substituting r from Step 1 and 胃 from the problem into the equation, solve the equation for the area A. This gives the area covered by the windshield wiper in square inches.

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