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10th Class Mathematics Mensuration Question Bank Mensuration

  • question_answer
    The ratio of the radii of two cylinders is \[1:\sqrt{3}\] and their heights are in the ratio 2 : 3 . The ratio of their volumes is

    A)  1 : 9                      

    B)         2 : 9  

    C)  4 : 9                                      

    D)  5 : 9

    Correct Answer: B

    Solution :

     
    Cylinder I Cylinder II
    \[r=x\] \[r=\sqrt{3}x\] [in the ratio \[1:\sqrt{3}\]]
    \[h=2y\] \[h=3y\] [in the ratio \[2:3\]]
    Volume, \[{{V}_{1}}=\pi .\,{{x}^{2}}.2y\] Volume, \[{{V}_{2}}=\pi .\,3{{x}^{2}}.3y\] \[\therefore \] s \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{2\pi \,{{x}^{2}}y}{9\pi \,{{x}^{2}}y}=\frac{2}{9}\]


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