Final answer:
The sector area of a circle with a radius of 50 meters and a central angle of π/3 radians is approximately 1310 square meters, after rounding to three significant figures.
Step-by-step explanation:
The question asks to find the sector area subtended by a central angle of π/3 radians (approximately 60°) in a circle with a radius of 50 meters. To find the sector area, we can use the formula for the area of a sector of a circle, which is A = ½ r² θ, where A represents the area, r is the radius of the circle, and θ is the central angle in radians.
For a circle with a radius of 50 meters, and a central angle of π/3 radians, the sector area A is calculated as follows:
- A = ½ × (50 m)² × (π/3 radians).
- A = ½ × 2500 m² × (π/3).
- A = 1250 m² × π/3.
- A = (1250/3) m² × π.
- A = approximately 1309 m² (after calculating with π ≈ 3.14159).
Considering significant figures, since the radius was given as a whole number without decimal places, the final answer can be rounded to three significant figures as 1310 m².