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

  • question_answer
    The radii of two circles are \[4\,cm\]and \[3\,cm\]respectively. The diameter of the circle having area equal to the sum of the areas of the two circles (in cm) is:          (NCERT EXEMPLAR; CBSE 2020)

    A) 5

    B) 7

    C) 10

    D) 14

    Correct Answer: C

    Solution :

    [c]  \[\pi {{R}^{2}}=\pi r_{1}^{2}+\pi r_{2}^{2}\]
    \[=\pi [r_{1}^{2}+r_{2}^{2}]=\pi \,[{{4}^{2}}+{{3}^{2}}]\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,{{R}^{2}}=25\]
    \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,R=25\]
    \[\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,d=5\times 2=10\]


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