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

  • question_answer
    In the given figure, a semicircle is drawn with O as centre and AB as diameter. Semicircles are drawn with AO and OB as diameters. If \[AB=28\text{ }m,\]find the perimeter of the shaded region. \[\left[ Use\,\,\pi =\frac{22}{7} \right]\]                        

    A)  \[70\text{ }m\]           

    B)  \[105\text{ }m\]         

    C)  \[88\text{ }m\]         

    D)         \[85\text{ }m\]

    Correct Answer: C

    Solution :

    We have,             \[AB=28\,m\,\,\Rightarrow \,AO=OB=14\,m\] Radius of semicircle with diameter AB (R)                                                      \[=\frac{28}{2}=14\,m\] Radius of semicircle with diameter AO \[({{r}_{1}})\]                                                 \[=\frac{14}{2}=7\,m\]      Perimeter of shaded region \[=\pi R+\pi {{r}_{1}}+\pi {{r}_{1}}\] \[=\pi \,(14+7+7)=\frac{22}{7}\times 28=88\,m\]


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