Solve the problem.
-What is the difference in area covered by a single 1 -inch windshield wiper operating with a central angle of $125 ^ { \circ }$ compared to a pair of 9 -inch wipers operating together each having a central angle of $119 ^ { \circ }$ ? Round to the nearest hundredth.
A) $172.14 \mathrm { in } ^ { 2 }$
B) $167.14 \mathrm { in. } ^ { 2 }$
C) $169.32 \mathrm { in. } { } ^ { 2 }$
D) $83.03 \mathrm { in } { } ^ { 2 }$

Question

Quizplus · Accepted Answer

The area of a sector is given by $\frac{\theta}{360} \times \pi \times r^2$. For the 1-inch wiper: $\frac{125}{360} \times \pi \times 1^2 \approx 1.09 \, \text{in}^2$. For each 9-inch wiper: $\frac{119}{360} \times \pi \times 9^2 \approx 84.11 \, \text{in}^2$. For two wipers: $2 \times 84.11 = 168.22 \, \text{in}^2$. The difference is $168.22 - 1.09 = 167.13 \, \text{in}^2$, rounded to $167.14 \, \text{in}^2$.

Solve the Problem 125∘125 ^ { \circ }125∘ Compared to a Pair of 9 -Inch Wipers Operating Together

Solve the Problem $125 ^ { \circ }$ Compared to a Pair of 9 -Inch Wipers Operating Together