Question

An automobile windshield wiper 26 inches long rotates through an

angle of 60°. If the rubber part of the blade covers only the last 20
inches of the wiper, find the area of the windshield cleaned by the
windshield wiper.

Answer 1

`\approx 209.44\:\mathrm{in^2}`

Explanation:

The area of a sector with radius
`r` and central angle
`\theta` is given by
`A{sec}=r^2\pi\cdot (\theta)/(360^(\circ))`. Note that a sector is a part of a circle which is the area created by the windshield wiper.

We're given:

• 
  `r=20`
• 
  `\theta=60^(\circ)`

Substituting given values, we have:

`A=20^2\pi\cdot (60)/(360),\\\\A=(20^2\pi)/(6),\\\\A=209.439510239\approx \boxed{209.44\:\mathrm{in^2}}` (round as necessary).