question_answer

Find the area of a segment of a circle of radius \[21\text{ }cm\] if the arc of the segment has a measure of \[{{60}^{o}}\]. (Take \[\sqrt{3}=1.73\])

A)  \[45.27\,c{{m}^{2}}\]                    

B)  \[40.8\,c{{m}^{2}}\]      

C)         \[40.27\,c{{m}^{2}}\]   

D)         \[42.07\,c{{m}^{2}}\]    

Correct Answer: C

Solution :

  Area of sector \[OAB=\frac{{{x}^{o}}}{{{360}^{o}}}\times \pi {{r}^{2}}\]                 \[=\frac{{{60}^{o}}}{{{360}^{o}}}\times \frac{22}{7}\times 21\times 21\,c{{m}^{2}}\]                 \[=231\,c{{m}^{2}}\] Area of \[\Delta \,\,OAB=\frac{\sqrt{3}}{4}\,{{r}^{2}}\]                 \[=\frac{\sqrt{3}}{4}\times 21\times 21\,c{{m}^{2}}\]                 \[=190.73\,c{{m}^{2}}\] \[\therefore \]Area of shaded region = Area of sector OAB - Area of \[\Delta \,OAB\] \[=(231-190.73)\,c{{m}^{2}}\]                                 \[=40.27\,c{{m}^{2}}\]