Question

The length of arc subtending an angle of ${135}^{\circ }$ at the center of the circle with radius $4\text{cm}=$

• A. $1.5\pi \text{cm}$
• B. $3\pi \text{cm}$
• C. $2.5\pi \text{cm}$

Answer 1

The correct option is B $3\pi \text{cm}$

We know the relation for length of arc subtending an angle $\alpha$(in degrees):
$l=\frac{\alpha }{{360}^{\circ }}\times 2\pi r$
Here, $r=4\text{cm},\alpha ={135}^{\circ }$

$\Rightarrow l=\frac{{135}^{\circ }}{{360}^{\circ }}\times 2\pi \times 4$

$\Rightarrow l=\frac{3}{8}\times 2\pi \times 4=3\pi \text{cm}$