What is the area of a sector with a central angle of 160 degrees and a diameter of 58m?

To find the area of a sector, we can use the formula:

Area of Sector = (θ / 360) × π × r²

where:

• θ is the central angle in degrees
• r is the radius of the circle

First, we need to find the radius of the circle. Given that the diameter is 58m, we can calculate the radius as follows:

r = diameter / 2

r = 58m / 2 = 29m

Now that we have the radius, we can substitute the values into the area of the sector formula:

Area of Sector = (160 / 360) × π × (29)²

Calculating the area step-by-step:

1. First, calculate (29)²: 29² = 841
2. Now substitute into the formula: Area of Sector = (160 / 360) × π × 841
3. Calculate (160 / 360): 160 / 360 = 0.4444 (approx)
4. Now, multiply: Area of Sector = 0.4444 × π × 841
5. Using π as approximately 3.14, we get:
6. Area of Sector ≈ 0.4444 × 3.14 × 841 ≈ 1,167.4608

Thus, the area of the sector is approximately 1,167.46 m².