Question

Given

$r=\frac{1}{\pi }units$

In the above figure,

Length of arc AB = 1 unit

• A. True
• B. False

Answer 1

The correct option is B

False

Applying the formula L = $r\Theta$ to find the length of arc, $\Theta$ should be in radian. Here $\Theta ={\pi }^o$ is given in degree. We will first convert to radian and use the relation L = $r\Theta$.
$1^o=\frac{\pi }{180}radian$
${\pi }^o=\pi$$\times$$\frac{\pi }{{180}^o}radian$
$=\frac{{\pi }^2}{180}radian$
$\Rightarrow L=r\Theta$
$=\frac{1}{\pi }\times$ $\frac{{\pi }^2}{180}$

$=\frac{\pi }{180}$
Key steps: Knowing that in the relation
$L=r\Theta ,\Theta$ is in radian

Method 2

We know ${360}^{\circ }$ corresponds to $2\pi r$ arc length