A) \[{{r}^{2}}(\pi -2)\,sq.\,units\]
B) \[2r(2-\pi )\,sq.\,units\]
C) \[\pi ({{r}^{2}}-2)\,sq.\,units\]
D) \[(\pi {{r}^{2}}-8r)sq.\,units\]
Correct Answer: A
Solution :
Clearly, area of unshaded region = Area of circle - Area of square RSTV But, diameter of circle = diagonal of square or \[2r=\sqrt{2}\,\,l\] or \[r=\frac{1}{\sqrt{2}}\] or \[l=r\sqrt{2}\] Area of unshaded region \[=\pi \,{{r}^{2}}-{{l}^{2}}=\pi \,{{r}^{3}}-{{(r\sqrt{2})}^{2}}\] \[=\pi \,{{r}^{2}}-2{{r}^{2}}={{r}^{2}}\,(\pi -2)\,\]sq. units
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