CUET UG 2025 — General Test Geometry

The radius of the circle is 36 cm and the area of the sector is $72\pi$72π cm².

The area of a sector is given by:

$$\text{Area of sector} = \frac{\theta}{360°} \times \pi r^2$$Area of sector=360°θ​×πr2

where $\theta$θ is the angle of the sector in degrees.

$$72\pi = \frac{\theta}{360°} \times \pi \times (36)^2$$72π=360°θ​×π×(36)2

$$72\pi = \frac{\theta}{360°} \times \pi \times 1296$$72π=360°θ​×π×1296

$$72 = \frac{\theta}{360°} \times 1296$$72=360°θ​×1296

$$\frac{\theta}{360°} = \frac{72}{1296}$$360°θ​=129672​

$$\frac{\theta}{360°} = \frac{1}{18}$$360°θ​=181​

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The arc length is given by:

$$\text{Arc length} = \frac{\theta}{360°} \times 2\pi r$$Arc length=360°θ​×2πr

$$\text{Arc length} = \frac{1}{18} \times 2\pi \times 36$$Arc length=181​×2π×36

$$\text{Arc length} = \frac{1}{18} \times 72\pi$$Arc length=181​×72π

$\text{Arc length} = 4\pi$Arc length=4π cm

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Therefore, the answer is Option 1: $4\pi$4π cm.