Final answer:
The area of the sector of a circle with a radius of 13 meters formed by a central angle of 15° is 8.70 square meters when rounded to the hundredths place. This was calculated using the formula for the area of a sector of a circle and rounding the result to maintain the correct number of significant figures.
Step-by-step explanation:
To find the area of the sector of a circle with a radius of 13 meters formed by a central angle of 15°, we will use the formula for the area of a sector, which is (A = (theta/360) × π × r²) where θ is the central angle in degrees and r is the radius of the circle. Since we have θ = 15° and r = 13 m, we can plug these values into our formula:
A = (15/360) × π × (13²) = (15/360) × 3.1415927 × 169
A = (0.0416667) × 3.1415927 × 169
A = 8.69911156 square meters
However, we must respect the significant figures in the given measurements. Since the radius was provided with two significant figures (13), our final answer should also contain two significant figures. Therefore, we round to the hundredths place:
A = 8.70 square meters.