Final answer:
To find the arc length, the total sector area is calculated from given percentage, the central angle is determined from this area, and finally the arc length is computed using the central angle and the radius. The arc length is found to be 1.4 meters.
Step-by-step explanation:
The student is asking to find the length of an arc in a circle, given that the radius is 0.7 meters and 20% of the sector area is 0.920 square meters. To solve this, we will first determine the total area of the sector using the given percentage, then find the central angle corresponding to the total sector area, and finally calculate the arc length using this angle and the radius.
First, calculate the total sector area:
- Total sector area = Sector area mentioned / Percentage represented
- Total sector area = 0.920 m2 / 0.20 = 4.6 m2
Second, calculate the central angle:
- The total area of the circle A = π * r2, where r is the radius.
- A = 3.1415927... * (0.7 m)2 = 1.539 m2 (rounded to three significant figures).
- Central angle of the sector = (Sector area / Total area of the circle) * 360 degrees.
- Central angle = (4.6 m2 / 1.539 m2) * 360 degrees ≈ 1078 degrees.
Finally, calculate the arc length from the central angle:
- Arc length As = (Central angle in radians / 2π) * Circumference of the circle.
- Since 1078 degrees = 1078 * π / 180 radians,
- Arc length As = (1078 * π / 180) / (2π) * (2π * 0.7 m).
- Arc length As = 1.4 meters.
Therefore, the correct answer is C. 1.4 meters.