To find the area of a sector of a circle, you can use the formula:
Area of Sector = (θ/360) x πr²
Where:
- θ is the central angle of the sector in degrees
- r is the radius of the circle
In this case, the area of the circle is given as 36 m². We know that the area of a full circle is calculated as πr², which is equal to 36 m². Therefore, we can find the radius (r) of the circle using the formula:
πr² = 36 m²
r² = 36/π
r ≈ √(36/π) ≈ √(36)/√(π) ≈ 6/√(π)
Now, we need to find the area of the 40° sector of the circle. Plugging in the values into the formula, we get:
Area of Sector = (40/360) x π(6/√(π))²
Area of Sector = (1/9) x 36/π
Area of Sector = 4 m²
Therefore, the area of a 40° sector of this circle is 4 m², which corresponds to option D.
