A) \[\frac{1}{4}\left( \pi -2{{a}^{2}} \right)\]
B) \[\left( \frac{1}{4} \right)\left( \pi {{a}^{2}}-{{a}^{2}} \right)\]
C) \[\frac{{{a}^{2}}}{2}\]
D) \[{{a}^{2}}\left( \frac{\pi -2}{2} \right)\]
Correct Answer: C
Solution :
(c): Area of quadrant \[=\frac{1}{4}\pi {{a}^{2}}\]; Area of triangle \[ACB=\frac{{{a}^{2}}}{2}\] Area of segment AQB = Area of sector AQBC ? Area of \[\Delta \,ACB=\frac{\pi {{a}^{2}}}{4}-\frac{{{a}^{2}}}{2}=\frac{{{a}^{2}}}{4}[\pi -2]\] Area of semi ? circle \[=\frac{1}{2}\pi {{\left( \frac{a\sqrt{2}}{2} \right)}^{2}}=\frac{\pi {{a}^{2}}}{4}\] \[\therefore \] Area of required region \[=\frac{\pi {{a}^{2}}}{4}-\frac{{{a}^{2}}}{4}[\pi -2]\] \[=\frac{{{a}^{2}}}{2}\] sq. unitYou need to login to perform this action.
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