The area of the sector of a circle of radius 12 cm is 32 π cm² Find the length of the corresponding arc of the sector.

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 17 Jul 2023 Shift 4)

Answer 1

Given:

The area of a sector of a circle = 32 π cm²

Radius of circle (R) = 12 cm

Formula used:

Area of a sector = (π × R² × θ)/360

Lenght of an arc = (2 × π × R × θ)/360

Calculation:

Area of a sector = (π × R2 × θ)/360

⇒ 32π = (π × (12)2 × θ)/360

⇒ 32 × 360 = (144 × θ)

⇒ θ = (32 × 360)/144

⇒ θ = 80°

Lenght of an arc = (2 × π × R × θ)/360

⇒ (2 × π × 12 × 80)/360

⇒ (16/3) × π

∴ The correct answer is \(\frac{16}{3}\) π cm.

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