Geometry

Circles

Easy

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.

4π cm

3π cm

2 π cm

π cm

✅ Correct Option: 1

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

The area of a sector is given by:

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

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

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

$72\pi = \frac{\theta}{360°} \times \pi \times 1296$

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

$\frac{\theta}{360°} = \frac{72}{1296}$

$\frac{\theta}{360°} = \frac{1}{18}$

The arc length is given by:

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

$\text{Arc length} = \frac{1}{18} \times 2\pi \times 36$

$\text{Arc length} = \frac{1}{18} \times 72\pi$

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

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

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Solution

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CUET General Test Past Year Questions (Topic-Wise)

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.