Question

What is the difference in area covered by a single 3 inch windshield wiper operating with a central angle of 138 degrees compared to a pair of 5 inch wipers operating together each having a central angle of 114 degrees?

Answer 1

38.9 square inches.

Explanation:

We are asked to find the difference in area covered by a single 3 inch windshield wiper operating with a central angle of 138 degrees compared to a pair of 5 inch wipers operating together each having a central angle of 114 degrees.

We will use area of sector formula to solve our given problem as:

`\text{Area of sector}=(\theta)/(360)* \pi r^2`, where, r represents radius and theta represents central angle.

Let us find area of sector with central angle 140 degree and radius 3 inch.

`\text{Area of sector}=(138)/(360)* \pi (3)^2`

`\text{Area of sector}=(138)/(360)* 9\pi`

`\text{Area of sector}=10.83849`

Now, we will find area of sector with central angle 114 degree and radius 5 inch and multiply by 2 as:

`\text{Area of sector}=2((114)/(360)* \pi (5)^2)`

`\text{Area of sector}=2((114)/(360)* 25\pi)`

`\text{Area of sector}=(114)/(360)* 50\pi`

`\text{Area of sector}=49.74188`

Let us find difference of area as shown below:

`\text{Difference of areas}=49.74188-10.83849`

`\text{Difference of areas}=38.90339`

`\text{Difference of areas}\approx 38.9`

Therefore, the difference in area covered is approximately 38.9 square inches.