# 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.

A car’s rear windshield wiper rotates ${125}^{\left(}circ\right)$ 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.
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Aamina Herring

Given:
$\theta ={125}^{\circ }$
${r}_{1}=25$ inches
${r}_{2}=14$ inches
$r={r}_{1}-{r}_{2}=25-14=11$ inches
$\theta ={125}^{\circ }\ast \pi /{180}^{\circ }\approx 2.1817$ radians
$1/2{r}^{2}\theta =1/2\ast {11}^{2}\ast 2.1817=131.993$
$1/2{r}^{\left(2/1\theta \right)}=1/2\ast {25}^{2}\ast 2.1817=681.781$
681.781-131.993=549.788