How would I calculate the area of a sector of a circle with radius 2 m that subtends an angle pi/3
π/3 is 1/6 of a complete rotation ...... (π/3)÷(2π)= 1/6)
So take the area of the whole circle , then divide by 6
To calculate the area of a sector of a circle, you can use the formula:
Area of sector = (angle/360°) * π * r²
In this case, the radius of the circle is 2 m and the angle subtended by the sector is π/3.
Calculating step-by-step:
1. Convert the angle from radians to degrees.
angle in degrees = (angle in radians) * (180 / π)
angle in degrees = (π/3) * (180 / π)
angle in degrees = 60°
2. Substitute the values in the formula:
Area of sector = (60°/360°) * π * (2m)²
Area of sector = (1/6) * π * 4 m²
Area of sector = (2/3) * π m²
Area of sector ≈ 2.094 m²
Therefore, the area of the sector with a radius of 2 m that subtends an angle π/3 is approximately 2.094 square meters.
To calculate the area of a sector of a circle, you need to use the formula:
Area of Sector = (θ/2) × r²,
where θ is the angle in radians, and r is the radius of the circle.
In this case, the angle is π/3 and the radius is 2 m. Plugging these values into the formula, we get:
Area of Sector = (π/3/2) × 2²
= (π/6) × 4
= (4π/6)
= (2π/3).
Therefore, the area of the sector is (2π/3) square meters.