What is the area of a sector with a central angle of 185° and a diameter of 6.4 m? Round the answer to the nearest tenth.
To find the area of the sector, we first need to find the radius of the circle. Since the diameter is 6.4 m, the radius is half of that, so the radius is 6.4 / 2 = 3.2 m.
Next, we need to find the area of the whole circle:
A = πr^2
A = π(3.2)^2
A = π(10.24)
A = 32.153 m^2
Now we need to find the area of the sector:
Sector Area = (θ/360) * A
Sector Area = (185/360) * 32.153
Sector Area = (0.5139) * 32.153
Sector Area ≈ 16.541 m^2
Therefore, the area of the sector with a central angle of 185° and a diameter of 6.4 m is approximately 16.5 m^2 (rounded to the nearest tenth).