10th Class Mathematics Areas Related to Circles Question Bank Case Based (MCQs) - Areas Related to Circles

  • question_answer
    Study Case : Q. 16 to 20
    Shiva made a painting on a square chart paper ABCD. The painting is made up of squares, semi-circular arcs (painted with flowers) and arcs of quadrant of circles as shown below. He painted the same type of region with same colours.
    Based on the above information, answer the following questions:       
    Find the total area of the region which is painted with flowers:                                         

    A) \[90.8\,c{{m}^{2}}\]

    B) \[100.57\,c{{m}^{2}}\]

    C) \[\text{1}0\text{5}.\text{6 c}{{\text{m}}^{\text{2}}}\]

    D) \[\text{111}.\text{2}0\text{ c}{{\text{m}}^{\text{2}}}\]

    Correct Answer: B

    Solution :

    Region which is painted with flowers are 4 semi-circles of diameter \[8cm,\] i.e., 2 circles of radius \[4cm\] each.
    \[\therefore \] Total area of region which is painted with flowers
    \[=2\times \pi {{r}^{2}}=2\times \frac{22}{7}\times 4\times 4=100.57c{{m}^{2}}\]
    So, option [b] is correct.

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