Answer :
The area of the sector is 4.244 m².
Option A is the correct answer.
We have,
To find the area of a sector, you can use the formula:
Area = (θ/360) * π * r²
Where:
θ is the central angle in degrees
r is the radius of the sector
Given:
Central angle (θ) = 210 degrees
Diameter = 4.6 m
To find the radius (r), we divide the diameter by 2:
r = diameter / 2 = 4.6 m / 2 = 2.3 m
Substituting the values into the formula, we get:
Area = (210/360) * π * (2.3)²
Calculating this expression:
Area = (0.5833) * 3.14159 * (2.3)²
Area ≈ 4.244 m²
Rounding to the nearest tenth, the area is approximately 4.2 m^2.
Therefore,
The area of the sector is 4.244 m².
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