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SSC Sample Paper Mock Test-4 SSC CGL Tear-II Paper-1

  • question_answer
    If a wire is bent into the shape of a square, the area of the square is 81 sq cm. When the wire is bent into a semi-circular shape, the area of the semi-circle (taking \[\pi =\frac{22}{7}\])is

    A)  \[154\,\,c{{m}^{2}}\]             

    B)  \[77\,\,c{{m}^{2}}\]

    C)  \[44\,\,c{{m}^{2}}\]               

    D)  \[22\,\,c{{m}^{2}}\]

    Correct Answer: B

    Solution :

    The length of wire = Perimeter of tha square \[=4\times \sqrt{\text{Area}\,\,\text{of}\,\text{square}}=4\times \sqrt{81}=4\times 9=36\,cm\]Now, perimeter of semi-circular shape = 36 cm \[\Rightarrow \]   \[(\pi \times r+2r)=36\,\,cm\] \[\Rightarrow \]   \[r\left( \frac{22}{7}+2 \right)=36\,\,cm\] \[\Rightarrow \]\[r\times \frac{36}{7}=36\,\,cm\]\[\Rightarrow \]\[r=\frac{36\times 7}{36}=7\,\,cm\] \[\therefore \]Required area \[=\frac{\pi {{r}^{2}}}{2}=\frac{22\times 7\times 7}{7\times 2}=77\,\,c{{m}^{2}}\]


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