Question

An arc of a circle of radius 6 cm subtends an angle of $30^\circ$ at the centre. The measure of the corresponding arc will be

• A. $\dfrac{\pi}{4}$ cm
• B. $\dfrac{\pi}{3}$ cm
• C. $\dfrac{\pi}{2}$ cm
• D. $\pi$ cm

Hint:

Arc length depends on the central angle: $\dfrac{\theta}{360^\circ} \times 2\pi r$. Always convert the angle into a fraction of 360°.

Answer 1

The Correct Option is B

Step 1: Formula for length of an arc. 
\[ \text{Length of arc} = \dfrac{\theta}{360^\circ} \times 2\pi r \] Step 2: Substitute the given values. 
\[ \theta = 30^\circ, \quad r = 6 \text{ cm} \] \[ \text{Arc length} = \dfrac{30}{360} \times 2\pi \times 6 \] Step 3: Simplify. 
\[ = \dfrac{1}{12} \times 12\pi = \dfrac{\pi}{1} = \pi \] Wait — we simplify carefully: \[ \dfrac{30}{360} = \dfrac{1}{12}, \quad 2\pi \times 6 = 12\pi \] \[ \text{Arc length} = \dfrac{1}{12} \times 12\pi = \pi \text{ cm} \] Step 4: Correct the simplification (angle check). 
Oops — on rechecking, angle \(30^\circ\) gives: \[ \text{Arc length} = \dfrac{30}{360} \times 2\pi \times 6 = \dfrac{1}{12} \times 12\pi = \pi \text{ cm} \] So the correct answer is actually (D) π cm. 
Step 5: Conclusion. 
The measure of the arc = $\pi$ cm.