Find the area of a sector with an arc length of 44 cm, which subtends a central angle of 30°.

Question

Accepted Answer

Given:
- Arc length (L) = 44 cm
- Central angle (θ) = 30°

Step 1: Convert the central angle to radians.
θ (in radians) = (30 × π) / 180 = π/6

Step 2: Use the arc length formula:
L = r × θ
=> r = L / θ = 44 / (π/6) = 44 × 6 / π = 264 / π cm

Step 3: Calculate the area of the sector using the formula:
Area = (1/2) × r² × θ
= (1/2) × (264/π)² × (π/6)
= (1/2) × (69696 / π²) × (π/6)
= (1/2) × (69696 / π) × (1/6)
= (69696) / (12π)

Step 4: Calculate numerical value:
π ≈ 3.1416
Area ≈ 69696 / (12 × 3.1416) ≈ 69696 / 37.6992 ≈ 1848.0 cm²

Therefore, the area of the sector is approximately 1848 cm².

Note: None of the provided options match the correct answer exactly. The correct area is approximately 1848 cm².

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