Final answer:
The area of the sector bounded by a 45° arc in a circle with a 10-meter radius is exactly (25π)/4 m² in simplest form.
Step-by-step explanation:
The question is asking for the area of a sector formed by a 45° arc in a circle where the radius (r) is 10 meters. The formula to find the area of a sector is A = (θ/360)×πr², where θ is the central angle in degrees. In this case, θ = 45°.
First, we convert the angle to radians, since one full circle (360°) is equivalent to 2π radians. Therefore, 45° is (45/360)×2π = π/4 radians.
Now we can calculate the area of the sector as follows:
A = (π/4)×π×10²
A = (π²/4)×100
A = (25π²)/4
Since we want the exact answer in simplest form, we leave π as it is, and the final answer is:
A = (25π)/4 m²