10th Class Mathematics Surface Areas and Volumes Question Bank Surface Area and Volume (Mensuration)

  • question_answer The ratio of radii of a cylinder to that of a cone is \[1:2\] If their heights are equal, find the ratio of their volumes?

    A)  \[1:3\]                          

    B)  \[2:3\]         

    C)  \[3:4\]   

    D)  \[3:1\]

    Correct Answer: C

    Solution :

    (c): Let the radius of cylinder = r Then, the radius of cone \[=R=2r\] \[\therefore \]      \[{{\left( \frac{r}{R} \right)}^{2}}=\frac{1}{4}\] Then, as per question. Ratio \[=\frac{\pi {{r}^{2}}h}{\frac{\pi {{R}^{2}}h}{3}}=\frac{2\pi {{r}^{2}}h}{\pi {{R}^{2}}h}=\frac{3{{r}^{2}}}{{{R}^{2}}}=3:4\]                         

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