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SSC Sample Paper Mock Test-12 SSC CGL Tear-II Paper-1

  • question_answer
    If the height of a given cone be doubled and radius of the base remains the same, the ratio of the volume of the given cone to that of the second cone will be

    A) 2 : 1     

    B)  1 : 8  

    C)  1 : 2    

    D)  8 : 1

    Correct Answer: C

    Solution :

    Case I
    When height \[={{h}_{1}},\]radius \[={{r}_{1}},\]
    Volume of the cone \[{{V}_{1}}=\frac{1}{3}\pi r_{1}^{2}{{h}_{1}}\]
    Case II
    When height \[{{h}_{2}}=2{{h}_{1}},\] radius\[{{r}_{2}}=2{{r}_{1}}\]
    \[\therefore \]Volume of the cone \[{{V}_{2}}=\frac{1}{3}\pi r_{1}^{2}\cdot 2{{h}_{1}}\]
    \[\therefore \]The required ratio = 1 : 2


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