To determine the distance traveled by the tip of each blade in a single full revolution, we can follow these steps:
1. Understand the Problem:
- Each blade of the wind turbine describes a circle as it rotates.
- We need to find the distance traveled by the tip of one blade during one complete revolution.
2. Recall the Relationship:
- For a circle, the distance traveled around the edge (circumference) can be calculated using the formula for the circumference of a circle:
[tex]\[
C = 2 \pi r
\][/tex]
where [tex]\( C \)[/tex] is the circumference and [tex]\( r \)[/tex] is the radius of the circle.
3. Identify the Radius:
- The length of each blade acts as the radius of the circular path described by the tip of each blade.
- Given the blade length (radius, [tex]\( r \)[/tex]) is 4 meters.
4. Calculate the Circumference:
- Substituting [tex]\( r = 4 \)[/tex] meters into the circumference formula, we get:
[tex]\[
C = 2 \pi \times 4
\][/tex]
5. Perform the Multiplication:
- Calculating the above expression:
[tex]\[
C = 2 \times \pi \times 4
\][/tex]
- This simplifies to:
[tex]\[
C = 8 \pi
\][/tex]
6. Use the Value of [tex]\(\pi\)[/tex]:
- Approximating [tex]\(\pi \approx 3.14159\)[/tex], we further calculate:
[tex]\[
C \approx 8 \times 3.14159 = 25.13272
\][/tex]
Therefore, the distance traveled by the tip of each blade in one full revolution is approximately [tex]\( 25.1327 \)[/tex] meters.
