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6th Class Mathematics Mensuration Question Bank Menstruation

  • question_answer
    DIRECTIONS: Passage-1 Read the passage(s) given below and answer the questions that follow. Read the information given below. A circular disc of area \[{{A}_{1}}\] is given with its radius as the diameter for a circular disc of area \[{{A}_{2}}\] is cut out of it. The area of the remaining disc is denoted by \[{{A}_{3}}\] then (i) \[{{A}_{1}}{{A}_{3}}<16A_{2}^{2}\] (ii)\[{{A}_{1}}{{A}_{3}}\,>16A_{2}^{2}\] (iii) \[{{A}_{1}}{{A}_{3}}=16A_{2}^{2}\] Which of the following is correct?

    A)  Only (i)          

    B)    Only (ii)

    C)  Only (iii)        

    D)    None of these

    Correct Answer: A

    Solution :

         \[{{A}_{1}}=\pi {{R}^{2}},\,\,{{A}_{2}}=\frac{\pi {{R}^{2}}}{4}\] \[\therefore \]    \[{{A}_{3}}=\pi {{R}^{2}}-\frac{\pi {{R}^{2}}}{4}=\frac{3\pi {{R}^{2}}}{4}\] \[\therefore \]    \[{{A}_{1}}{{A}_{3}}=\pi {{R}^{2}}\times \frac{3}{4}\,\pi {{R}^{2}}\] \[=\frac{3}{4}\,{{\pi }^{2}}{{R}^{4}}=3\pi {{R}^{2}}{{A}^{2}}\] \[=3\times 4{{A}_{2}}\times {{A}_{2}}=12A_{2}^{2}\] \[\Rightarrow \,\,{{A}_{1}}{{A}_{3}}<16\,A_{2}^{2}\]


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