question_answer

Find the area of a segment of a circle of radius 21 cm if the angle made by the arc of the segment has a measure of\[~\text{6}0{}^\circ \].

A)  \[\text{45}.\text{27 c}{{\text{m}}^{\text{2}}}\]               

B) \[\text{4}0.\text{27 c}{{\text{m}}^{\text{2}}}\]

C)  \[\text{4}0.\text{8 c}{{\text{m}}^{\text{2}}}\]                                  

D) \[\text{44}.\text{27 c}{{\text{m}}^{\text{2}}}\]

Correct Answer: B

Solution :

  Area of sector \[L.C.M.\] \[\frac{6}{14}and\frac{2}{7}\] \[\Rightarrow \]Area of \[\frac{L.C.M.(6,2)}{H.C.F.(14,7)}=\frac{6}{7}\] \[\text{7}\times \text{13}+\text{13}=\text{1}0\text{4}=\text{23}\times \text{13}\]Area of sector = 231 - 190.73 \[\therefore \]