Question

An minor arc subtends an angle of ${60}^{\circ }$ at the centre of the circle with radius $3$ units. What is the arc length of the major sector?

• A. $4\pi \mathrm{units}$
• B. $5\pi \mathrm{units}$
• C. $6\pi \mathrm{units}$
• D. $7\pi \mathrm{units}$

Answer 1

The correct option is B $5\pi \mathrm{units}$

Angle subtended by the major sector at the centre of the circle $={360}^{\circ }-{60}^{\circ }={300}^{\circ }$
Hence, arc length $\frac{{360}^{\circ }-{300}^{\circ }}{{360}^{\circ }}\times \pi \times 6=5\pi$ units.