Question

Length of an arc of a sector of angle 45° when the radius of the circle is 3 cm, is:

• A. \( \frac{5\pi}{4} \, \text{cm} \)
• B. \( \frac{3\pi}{4} \, \text{cm} \)
• C. \( \frac{\pi}{4} \, \text{cm} \)
• D. \( \frac{\pi}{2} \, \text{cm} \)

Hint:

For the length of an arc, use the formula \( L = \frac{\theta}{360} \times 2\pi r \), where \( \theta \) is the angle in degrees and \( r \) is the radius.

Answer 1

The Correct Option is B

Step 1: Formula for the Length of an Arc. The length \( L \) of an arc of a sector is given by the formula: \[ L = \frac{\theta}{360} \times 2\pi r \] where \( \theta \) is the central angle, and \( r \) is the radius of the circle. 
Step 2: Substituting the Given Values. Here, the radius \( r = 3 \, \text{cm} \) and the angle \( \theta = 45^\circ \). Substituting these values into the formula, we get: \[ L = \frac{45}{360} \times 2 \times 3.14 \times 3 \] \[ L = \frac{45}{360} \times 18.84 = \frac{1}{8} \times 18.84 \] \[ L = \frac{3\pi}{4} \, \text{cm} \] 
Step 3: Conclusion. Thus, the length of the arc is \( \frac{3\pi}{4} \, \text{cm} \).