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What is the area of a sector with a central angle of 210 degrees and a diameter of 4.6 m? Round the answer to the nearest tenth.

A. 4.2 m²
B. 9.7 m²
C. 14.5 m²
D. 38.8 m²

Answer :

9.7 is the 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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