Question

Find the perimeter of the minor sector $OAB$ shown below.

cm

Answer 1

Given, the radius of a circle is $r=OA=OB=7\text{cm}$
and the angle subtentded by $\stackrel{⌢}{AB}$ is $\theta ={90}^{\circ }.$

Step 1:
$\text{Length of the arc}\stackrel{⌢}{AB}=\frac{\theta }{{360}^{\circ }}\times 2\pi r$

$=\frac{{90}^{\circ }}{{360}^{\circ }}\times 2\pi \times 7$

$=\frac{{90}^{\circ }}{4\times {90}^{\circ }}\times 2\pi \times 7$

$=\frac{1}{4}\times 2\pi \times 7$
​​​​​​​
$=\frac{1}{4}\times 2\times \frac{22}{7}\times 7$
​​​​​​​
$=11\text{cm}$

Step 2: Perimeter of the minor sector $OAB$
$=OA+OB+\stackrel{⌢}{AB}$
$=7+7+11$
$=25\text{cm}$

Hence, the perimeter of the minor sector $OAB$ is $25\text{cm}.$