Final answer:
To calculate the area of a sector, calculate the area of a full circle (πr²) and then multiply by the fraction of the circle the sector represents, which is determined by the central angle over 360 degrees. The given radius has four significant figures which allows for a more precise calculation of area.
Step-by-step explanation:
To find the area of the sector with a central angle of 225 degrees and a radius of 11.04 meters, we first need to understand that the area of a full circle is given by πr², where π is approximately 3.1415927 and r is the radius. However, because we are only dealing with a sector and not the entire circle, we need to take into account the proportion of the circle that the sector represents. The central angle of the sector out of 360 degrees will give us this proportion.
First, calculate the area of the full circle using the given radius:
- A = πr² = (3.1415927…) × (11.04 m)²
Second, find the proportion of the circle that the sector covers:
- Proportion = Central Angle / Total Angle = 225° / 360° = 0.625
Finally, calculate the area of the sector by multiplying the area of the entire circle by the proportion:
- Sector Area = A × Proportion
Note that if the radius has only two significant figures, you would limit the calculated quantity accordingly, but in this problem, the radius is given to four significant figures, so we can maintain more precision in our answer. Calculating the exact value using the steps provided will give you the sector area in square meters.