question_answer

Find measure of central angle of the sector whose perimeter is 25 cm. and radius of the circle is 7 cm.

A) \[~45{}^\circ \]

B) \[~22.5{}^\circ \]         

C) \[~135{}^\circ \]

D) \[90{}^\circ \]

Correct Answer: D

Solution :

OA = OB =7 cm. Arc AB = (OA + OB + AB - OA=OB) \[=(25-2\times 7)cm.=11\,cm.\] \[\therefore \]\[\theta =\frac{l}{r}\]radian \[=\frac{11}{7}\]radian \[\because \]\[\pi \]radian \[={{180}^{o}}\] \[\therefore \]\[\frac{11}{7}\]radian \[=\left( \frac{18}{\pi }\times \frac{11}{7} \right)\] \[=\left( \frac{180}{22}\times \frac{11\times 7}{7} \right)={{90}^{o}}\]