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

Answer:

38.9 square inches.

Step-by-step 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:

$\text{Area of sector}=\frac{\theta}{360}\times \pi r^2$, where, r represents radius and theta represents central angle.

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

$\text{Area of sector}=\frac{138}{360}\times \pi (3)^2$

$\text{Area of sector}=\frac{138}{360}\times 9\pi$

$\text{Area of sector}=10.83849$

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

$\text{Area of sector}=2(\frac{114}{360}\times \pi (5)^2)$

$\text{Area of sector}=2(\frac{114}{360}\times 25\pi)$

$\text{Area of sector}=\frac{114}{360}\times 50\pi$

$\text{Area of sector}=49.74188$

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.