Question
Download Solution PDFThe 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
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.
Last updated on Jul 17, 2025
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