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

  • question_answer
    Study Case : Q. 6 to 10
    Sara hold a Japanese folding fan in her hand as shown in the figure. It is shaped like a sector of a circle and made of a thin material such as paper or feather. The inner and outer radii are \[\text{3 cm}\] and \[\text{5 cm}\] respectively. The fan has three colours i.e., red, blue and green.
    Based on the above information, answer the following questions:
    If the region containing blue colour makes an angle of \[80{}^\circ \]at the centre, then find the area of the region having blue colour.

    A) \[9.17\,c{{m}^{2}}\]

    B) \[10.1\,c{{m}^{2}}\]

    C) \[11.17\,c{{m}^{2}}\]

    D) \[13.17\,c{{m}^{2}}\]

    Correct Answer: C

    Solution :

    Area of the region containing blue colour      
    \[=\frac{22}{7}\times 5\times 5\times \frac{80{}^\circ }{360{}^\circ }-\frac{22}{7}\times 3\times 3\times \frac{80{}^\circ }{360{}^\circ }\]
    \[=\frac{22}{7}\times \frac{2}{9}\times [25-9]=\frac{44}{63}(16)=11.17c{{m}^{2}}\]          
    So, option [c] is correct.

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