The area of a sector of a circle of radius 36 cm is \(72\pi\) cm2. Find the length of the corresponding arc of the sector.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 4π cm
The area of a sector is half the product of the radius and the arc length, \(A=\frac{1}{2}rl\), just as a triangle’s area is half its base times its height. So the arc length follows from the area without finding the angle.
Putting the area \(72\pi\) and the radius 36 into the formula: \(72\pi=\frac{1}{2}\times36\times l\)
\(72\pi=18\,l\), so \(l=\frac{72\pi}{18}=4\pi\,\mathrm{cm}\)