Question

An arc of a circle makes a 36° angle at its centre. If the arc has length 26 cm, find the radius of the circle

Answer 1

The arc of the circle makes an angle of 36 degree at its center

Arc length = 26cm

The expression for the arc length of the circle is :

`\begin{gathered} \text{Arc length=2}\pi r((\theta)/(360)) \\ \text{Here we have }\theta=36\text{ , Arc length = 26 and we have to solve for r} \\ 26=2\Pi r((36)/(360)) \\ (26)/(2\Pi)=r((1)/(10)) \\ r=(13*10)/(3.14) \\ r=41.4\text{ cm} \end{gathered}`

So, the radius = 41.4cm