Question

The angle (in degrees) subtended at the centre of a circle of diameter $50$ cm by an arc of length $11$ cm is

• A. ${12}^{\circ }{25}^{\prime }$
• B. ${25}^{\circ }{12}^{\prime }$
• C. ${65}^{\circ }{32}^{\prime }$
• D. ${32}^{\circ }{65}^{\prime }$

Answer 1

The correct option is B ${25}^{\circ }{12}^{\prime }$

Given, $r=25$ cm and $l=11$ cm
${\theta }^c={\left(\frac{l}{r}\right)}^c\Rightarrow {\theta }^c={\left(\frac{11}{25}\right)}^c\Rightarrow \theta =(\frac{11}{25}\times \frac{{180}^{\circ }}{\pi })$
We know that $\pi =\frac{22}{7}$,
$\Rightarrow \theta ={\left(\frac{126}{5}\right)}^{\circ }={25}^{\circ }{\left(\frac{60}{5}\right)}^{\prime }\therefore \theta ={25}^{\circ }{12}^{\prime }$