Question

If the sector of a circle of diameter $10\text{cm}$ subtends an angle of ${144}^{\circ }$ at the centre, then the length of the arc of the sector is

• A. $2\pi \text{cm}$
• B. $4\pi \text{cm}$
• C. $5\pi \text{cm}$
• D. $6\pi \text{cm}$

Answer 1

The correct option is B $4\pi \text{cm}$

Given, diameter $=10cm$

So, radius, $r=\frac{d}{2}$

$r=5\text{cm}$

Angle subtended at the centre, $\theta ={144}^{\circ }$

Length of arc subtending angle $\theta =\frac{\theta }{360}\times 2\pi \times r$
$\therefore$ length $=$ $\frac{{144}^{\circ }}{{360}^{\circ }}\times 2\pi \times 5=4\pi cm$