10th Class Mathematics Areas Related to Circles Question Bank Areas Related to Circles

  • question_answer
                A steel wire when bent in the form of a square encloses an area of 121 sq. cm. If the same wire is bent into the form of a circle, find the area of the circle. [use \[\pi =\frac{22}{7}\]]                           

    A)  \[44\text{ }c{{m}^{2}}\]        

    B)        \[308\text{ }c{{m}^{2}}\]     

    C)                     \[77\text{ }c{{m}^{2}}\]        

    D)        \[154\text{ }c{{m}^{2}}\]    

    Correct Answer: D

    Solution :

    Area of Square = 121 sq. cm. \[\therefore \] Side of square = 11 cm \[\Rightarrow \] Perimeter of square \[=4\times side=44\text{ }cm\] \[\therefore \] Length of wire \[=44\text{ }cm.\] Now circumference of circle = 44 cm \[\Rightarrow \] \[2\pi r=44\Rightarrow r=\frac{44\times 7}{2\times 22}=7\] Area of circle \[=\pi \times {{(7)}^{2}}=154\,c{{m}^{2}}\]


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