question_answer

4 identical semicircles are drawn inside a big square as shown. Each side of the big square is 14cm long. Find the area of the shaded region. (Use\[\pi =\frac{22}{7}\].)

A)  \[\text{125}\,\text{c}{{\text{m}}^{\text{2}}}\]                                 

B)  \[\text{112 c}{{\text{m}}^{\text{2}}}\]

C)  \[\text{173}\,\text{c}{{\text{m}}^{\text{2}}}\]                                 

D)  \[\text{159 c}{{\text{m}}^{\text{2}}}\]

Correct Answer: B

Solution :

 Radius\[\text{4}0\text{8 }=\text{ 216 }\times \text{ 1 }+\text{ 192}\] Area of a \[\text{216 }=\text{ 192 }\times \text{ 1 }+\text{ 24}\]                                 \[\text{192 }=\text{ 24 }\times \text{ 8 }+\text{ }0\] Area of a \[{{6}^{x}}\]                                 \[{{6}^{x}}={{(2\times 3)}^{x}}={{2}^{x}}\times {{3}^{x}}\] Area of a \[\Rightarrow \]                                 \[{{6}^{x}}\] Area of shaded region \[\therefore \]                                 \[{{6}^{x}}\]