We appreciate your visit to 97 Windshield Wiper The arm and blade of a windshield wiper have a total length of 34 inches If the blade is 25 inches long. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
To calculate the area that a windshield wiper can clean with a 120° sweep and a 25-inch long blade, we use the area of a sector formula, involving the blade and arm length as the radius, and convert the sweep angle to radians for the calculation.
Explanation:
The question asks about the area that a windshield wiper can clean if it spans an angle of 120° and has a blade length of 25 inches. To find this area, we need to calculate the area of a sector of a circle. The formula to find the area of a sector is \( A = \frac{1}{2}r^2\theta \), where \( r \) is the radius and \( \theta \) is the angle in radians. Since the total length of the arm and blade is 34 inches and the blade is 25 inches long, the radius of the circle is 34 inches.
First, let's convert the angle from degrees to radians by using the conversion ratio \( \frac{\pi}{180} \).
\( 120\degree = 120 \times \frac{\pi}{180} = \frac{2\pi}{3} \, \text{radians} \)
Now we can calculate the area:
\( A = \frac{1}{2} \times (34\text{in})^2 \times \frac{2\pi}{3} \)
Calculating this gives us the area that the windshield wiper can clean.
Thanks for taking the time to read 97 Windshield Wiper The arm and blade of a windshield wiper have a total length of 34 inches If the blade is 25 inches long. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
Final answer:
To calculate the window area that the blade can clean, we need to find the length of the arc formed by the sweeping angle of 120° and then calculate the corresponding area of the sector.
Explanation:
To calculate the window area that the blade can clean, we need to find the length of the arc formed by the sweeping angle of 120° and then calculate the corresponding area of the sector. First, we need to find the length of the arc using the formula:
Arc Length = (angle/360°) * circumference of the circle
Since the total length of the arm and blade is 34 inches and the blade is 25 inches long, the arm must be 9 inches long. Therefore, the radius of the circle formed by the wiper is 9 inches. The circumference of the circle is given by 2πr, where r is the radius. Substituting the values, we find:
Circumference = 2 * 3.14 * 9 = 56.52 inches
The length of the arc can be calculated as:
Arc Length = (120/360) * 56.52 = 18.84 inches
Now, we can calculate the area of the sector formed by the arc using the formula:
Area of Sector = (angle/360°) * πr²
Substituting the values, we find:
Area of Sector = (120/360) * 3.14 * (9)^2 = 84.78 square inches
Therefore, the blade can clean a window area of 84.78 square inches.
Learn more about Calculating area of a sector here:
https://brainly.com/question/33739057
#SPJ12
