| The area of the shaded region in figure as shown below where ABCD is a square of side 12 cm is equal to |
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A) \[15.43c{{m}^{2}}\]
B) \[198c{{m}^{2}}\]
C) \[31.72c{{m}^{2}}\]
D) \[30.86c{{m}^{2}}\]
Correct Answer: D
Solution :
\[\because \]Area of square \[=\text{ }{{\left( Side \right)}^{2}}\] \[\therefore \] Area of square \[ABCD=12\times 12\] \[=144\text{ }c{{m}^{2}}\] \[\because \]Diameter of each circle \[=\frac{12}{2}=6\,cm\] [here, length = 12 cm] \[\therefore \] Radius of each circle \[\left( r \right)=\frac{6}{2}=3\,cm\] Area of one circle \[=\pi {{r}^{2}}\] \[=\frac{22}{7}\times 3\times =\frac{198}{7}c{{m}^{2}}\] Therefore, area of four circles \[=4\times \frac{198}{7}\] \[=\frac{792}{7}c{{m}^{2}}\] Hence, area of the shaded region = Area of square - Area of four circles \[=144-\frac{792}{7}=\frac{1008-792}{7}\]\[=\frac{216}{7}=30.86\,c{{m}^{2}}\]
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