The area of a sector of a circle of radius 36 cm is $72π\, cm^2$. Find the length of the corresponding arc of the sector.

4π cm

The correct answer is Option (1) → 4π cm

Given:

• Radius $r = 36$
• Area of sector $A = 72\pi\,cm^2$

Step 1: Formula for area of sector

$A = \frac{1}{2} r^2 \theta$

Where θ = central angle in radians.

$72\pi = \frac{1}{2} \cdot 36^2 \cdot \theta$

$72\pi = \frac{1}{2} \cdot 1296 \cdot \theta$

$72\pi = 648 \cdot \theta$

$\theta = \frac{72\pi}{648} = \frac{\pi}{9} \text{ radians}$

Step 2: Formula for arc length

$l = r \theta = 36 \cdot \frac{\pi}{9} = 4\pi \text{ cm}$